Equation Simplifier
Simplify any algebraic equation instantly. Enter your equation below and get a full step-by-step breakdown — from distribution and combining like terms all the way to the final simplified form.
Works with linear equations, quadratic equations, polynomial expressions, and rational equations.
Simplify Your Equation
Examples: 2x + 4 = 10, x^2 + 5x + 6 = 0, 3(x + 2) - x = 8
How to Simplify an Equation
Simplifying an equation means rewriting it in the most reduced, clean form while preserving its mathematical meaning. Here are the core steps:
Step 1 — Distribute Parentheses
Multiply any factor outside a bracket by each term inside. For example: 3(x + 2) becomes 3x + 6.
Step 2 — Combine Like Terms
Add or subtract terms that share the same variable and exponent. 3x + 2x simplifies to 5x.
Step 3 — Isolate the Variable
Move all variable terms to one side of the equation and all constants to the other using inverse operations (add/subtract, multiply/divide).
Step 4 — Divide by the Coefficient
If the variable has a coefficient other than 1, divide both sides to get the variable alone. 5x = 20 → x = 4.
Types of Equations This Simplifier Handles
Linear Equations
2x + 3 = 11 → x = 4
Single-variable equations where the highest power is 1.
Quadratic Equations
x² - 5x + 6 = 0 → x = 2, 3
Equations with an x² term, solvable by factoring or the quadratic formula.
Polynomial Equations
2x³ + x² - x
Higher-degree expressions simplified by factoring out common terms.
Rational Expressions
(x²-1)/(x+1) → x - 1
Fractions with polynomials in the numerator and denominator, simplified by cancellation.
Common Simplification Rules
| Rule | Before | After |
|---|---|---|
| Distributive Property | a(b + c) | ab + ac |
| Combine Like Terms | 3x + 2x + 5 | 5x + 5 |
| Cancel Common Factor | (x² - 4) / (x - 2) | x + 2 |
| Zero Product Property | x(x - 3) = 0 | x = 0 or x = 3 |
| Difference of Squares | x² - 9 | (x + 3)(x - 3) |
| Exponent Rule | x² · x³ | x⁵ |
Frequently Asked Questions
What is an equation simplifier?
An equation simplifier is a tool that takes a mathematical equation and reduces it to its simplest equivalent form by combining like terms, distributing factors, cancelling common terms, and applying algebraic identities.
How do you simplify an equation step by step?
To simplify an equation: (1) Distribute any parentheses, (2) Combine like terms on each side, (3) Move all variable terms to one side and constants to the other, (4) Divide both sides by the coefficient of the variable.
Can this simplifier handle quadratic equations?
Yes. The simplifier handles linear equations, quadratic equations (ax² + bx + c = 0), polynomial equations, and rational equations with full step-by-step breakdown.
What is the difference between simplifying and solving an equation?
Simplifying reduces an expression to its most compact form without finding variable values. Solving finds the actual values of variables. Our tool does both — it simplifies the expression and then solves for the unknown.
Can I simplify equations with fractions?
Yes. Enter equations with fractions directly, such as (x+1)/2 = 3. The simplifier will multiply through by the denominator, clear the fraction, combine terms, and solve step-by-step.