Scientific Notation Calculator

Equation Solver

Use this equation solver to isolate any variable in a linear equation, follow each algebraic step, and verify the answer by substitution back into the original equation.

Solve one-variable linear equationsStep-by-step algebraic breakdownVerify answers by substitution

Equation Solver

Solve one-variable equations with exact linear/quadratic handling and numerical roots for broader equations.

Ready

Supports one variable, implicit multiplication, powers, roots, logs, and trig functions in radians.

Step by Step

Result Summary

Solutions: x = 4
Equation: 2x + 3 = 11

Explore More Scientific Calculators

Related Calculators

Specialized tools for significant figures, exponents, roots, rounding, powers of ten, and equation solving.

Sig Figs Calculator Count significant figures in any expression and round to the precision you need. Free sig figs calculator with step-by-step output, rules, and worked examples. Square Root Calculator Find square roots, simplify radicals, and solve nested root expressions online. Free calculator with exact radical form, decimal output, and complex number support. Exponents Calculator Calculate any base–exponent expression and apply laws of exponents online. Free exponents calculator with negative, zero, and fractional exponents plus step-by-step solutions. Power of 10 Calculator Multiply or divide by any power of 10, convert between SI metric prefixes, and explore orders of magnitude. Free calculator with prefix table and worked examples. Rounding Calculator Round any number to the nearest integer, decimal place, or precision level. Free rounding calculator with half-up, banker's rounding, and truncation options plus worked examples.

Converter

Need a notation converter?

Convert between scientific notation, decimal notation, engineering notation, and E notation with clear formatting.

Open converter

Equation Solver

An equation solver finds the value of an unknown variable that makes both sides of an equation equal. Linear equations—those where the variable appears only to the first power—are the most common type in algebra, physics, and everyday problem-solving. This calculator accepts equations with one variable, simplifies both sides, isolates the variable through inverse operations, and returns the solution with every algebraic step explained.

What Is a Linear Equation?

A linear equation is a mathematical statement that two expressions are equal and where the variable appears only to the first power. The equation 3x + 5 = 20 states that 3x + 5 and 20 are equal for some specific value of x. Solving it means finding that value: subtracting 5 from both sides gives 3x = 15, and dividing by 3 gives x = 5. Substituting back confirms 3(5) + 5 = 20. Linear equations have exactly one solution, no solution, or infinitely many solutions depending on their structure. Recognizing each case and knowing which inverse operations to apply at each step is the core skill of algebraic equation solving.

How to Use the Equation Solver

Type the equation into the input field using x (or another variable) on either or both sides. The solver accepts standard arithmetic operators, fractions written as numerator/denominator, and parentheses for grouped terms. Valid inputs include: 3x + 5 = 20, 2(x − 3) = 4x + 1, and x/2 + 3 = 7.

Click Solve. The results panel displays the value of the variable and a numbered step-by-step solution showing each inverse operation applied. A substitution check confirms that the found value makes both sides of the original equation equal.

Worked Examples

Representative examples: 3x + 5 = 20 → x = 5; 2(x − 3) = 4x + 1 → x = −3.5; x/4 − 2 = 3 → x = 20; 5x = 3x + 14 → x = 7; and 0.5x + 1.2 = 3.7 → x = 5.

Common Equation Types

Common problems include solving for a variable in distance–rate–time formulas (d = r × t), isolating variables in Ohm's law (V = IR), solving percent equations, and working through two-step equations in algebra coursework.

Linear Equation Solving Methods

These tables cover the core steps and properties used to isolate a variable in one-variable linear equations.

One-step equations: addition and subtraction

To isolate a variable in a one-step additive equation, apply the inverse operation to both sides.

Equation	Inverse operation	Step result	Solution
x + 7 = 12	Subtract 7 from both sides	x = 12 − 7	x = 5
x − 4 = 9	Add 4 to both sides	x = 9 + 4	x = 13

One-step equations: multiplication and division

To isolate a variable in a one-step multiplicative equation, apply the inverse—dividing or multiplying both sides by the same non-zero value.

Equation	Inverse operation	Step result	Solution
4x = 28	Divide both sides by 4	x = 28 / 4	x = 7
x/3 = 5	Multiply both sides by 3	x = 5 × 3	x = 15

Two-step equations

Two-step equations need two inverse operations. Undo the addition or subtraction first, then undo the multiplication or division.

Equation	Step 1	Step 2	Solution
3x + 5 = 20	Subtract 5: 3x = 15	Divide by 3	x = 5
2x − 7 = 9	Add 7: 2x = 16	Divide by 2	x = 8

Variable on both sides

Collect all variable terms on one side and all constants on the other by adding or subtracting the smaller variable term from both sides.

Equation	Collect variable terms	Collect constants	Solution
5x = 3x + 14	5x − 3x = 14 → 2x = 14	Divide by 2	x = 7
6x − 2 = 4x + 8	2x = 10	Divide by 2	x = 5

Equations with parentheses

Use the distributive property to expand parentheses first, then collect like terms and isolate the variable.

Equation	Distribute	Collect terms	Solution
2(x + 3) = 10	2x + 6 = 10	2x = 4	x = 2
3(2x − 1) = 15	6x − 3 = 15	6x = 18	x = 3

Equations with fractions

Clear fractions by multiplying both sides by the least common denominator (LCD) of all fractional terms before solving.

Equation	LCD	Cleared equation	Solution
x/2 + 1 = 4	LCD = 2	x + 2 = 8	x = 6
x/3 − x/6 = 2	LCD = 6	2x − x = 12	x = 12

Verifying solutions by substitution

Always check your answer by substituting the value back into the original equation. If both sides are equal, the solution is verified.

Equation	Solution	Substitution check	Verified
3x + 5 = 20	x = 5	3(5) + 5 = 20 ✓	Yes
2x − 7 = 9	x = 8	2(8) − 7 = 9 ✓	Yes

Process

Calculation Workflow

Enter equation

Distribute and simplify

Isolate the variable

Verify by substitution

The solver parses the equation, distributes any parentheses, collects like terms, applies inverse operations step by step to isolate the variable, and confirms the result by substituting the solution back into the original equation.

Input Formats

Supported Formats

Input style	Example
Two-step equation	3x + 5 = 20
Variable on both sides	5x = 3x + 14
With parentheses	2(x − 3) = 4x + 1
With fractions	x/2 + 3 = 7

Reference

Common Scientific Constants

Back to calculator

Constant name	Symbol	Notation value	Unit
Speed of light	c	2.99792458 x 10^8	m/s
Gravitational constant	G	6.67430 x 10^-11	N m^2/kg^2
Avogadro constant	NA	6.02214076 x 10^23	mol^-1

Questions

Calculator FAQ

What is a linear equation?

A linear equation is one where the variable appears only to the first power and is not inside a radical, exponent, or denominator that contains the variable. Its graph is a straight line and it has at most one solution.

How do I solve an equation?

Isolate the variable by applying inverse operations to both sides. Undo addition and subtraction first, then undo multiplication and division. Every operation must be applied equally to both sides.

What does it mean to isolate a variable?

Isolating a variable means rearranging the equation so the variable stands alone on one side with a coefficient of 1. The other side then equals the solution.

What is the distributive property?

The distributive property states that a(b + c) = ab + ac. When an equation has parentheses, expand them using this property before combining like terms.

How do I solve 3x + 5 = 20?

Subtract 5 from both sides to get 3x = 15. Then divide both sides by 3 to get x = 5. Check: 3(5) + 5 = 20 confirms the solution.

How do I solve an equation with fractions?

Multiply both sides by the least common denominator of all fractions in the equation. This clears the fractions and leaves a simpler equation to solve.

What does 'no solution' mean in a linear equation?

A linear equation has no solution when the variable cancels out and the remaining constants are unequal. For example, 2x + 3 = 2x + 7 simplifies to 3 = 7, which is never true.

What does 'infinitely many solutions' mean?

An equation has infinitely many solutions when the variable cancels and the remaining statement is always true. For example, 3x + 6 = 3(x + 2) simplifies to 6 = 6, which is true for any value of x.

How do I check a solution?

Substitute the value back into the original equation and evaluate both sides. If both sides produce the same number, the solution is correct.

What are like terms?

Like terms contain the same variable raised to the same power. In 4x + 3x − 2, the terms 4x and 3x are like terms and combine to give 7x − 2.

What is a two-step equation?

A two-step equation requires exactly two inverse operations to isolate the variable. For example, 2x + 4 = 10 is solved by subtracting 4 (step 1) and then dividing by 2 (step 2).

How do I solve for x when it appears on both sides?

Move all x terms to one side by adding or subtracting the smaller x term from both sides. Then solve the resulting one-variable equation normally.

Can I solve equations with decimal coefficients?

Yes. Treat decimal coefficients the same as integers. You can optionally multiply both sides by a power of 10 to clear the decimals before solving, or work directly with the decimal values.

What operations can I apply to both sides of an equation?

You can add, subtract, multiply, or divide any non-zero value to both sides while preserving equality. Dividing by zero is not allowed.

What is the difference between an equation and an expression?

An expression is a combination of numbers and operators with no equals sign, such as 3x + 5. An equation asserts two expressions are equal—3x + 5 = 20—and can be solved for the variable.