Free Equation Solver - Step-by-Step Solutions Online

Solve any linear equation, quadratic equation, or system of equations with our comprehensive online equation solver. Get detailed step-by-step solutions that help you understand the solving process, making it perfect for homework help, test preparation, and learning algebra.

Our equation calculator supports multiple formats and provides clear explanations for each step, helping students master equation-solving techniques. Whether you're working with simple linear equations or complex polynomial systems, our solver delivers accurate results with educational value.

Solve Your Equation

Use standard mathematical notation. Example: 2x + 5 = 11

Quick Examples:

Understanding Different Types of Equations

Linear Equations

Linear equations are first-degree equations where the variable appears only to the first power. They form straight lines when graphed and have at most one solution.

Solving Methods:

  • • Isolate the variable by performing inverse operations
  • • Add or subtract the same value from both sides
  • • Multiply or divide both sides by the same non-zero value
  • • Combine like terms when necessary

Quadratic Equations

Quadratic equations are second-degree equations with the form ax² + bx + c = 0. They can have zero, one, or two real solutions.

Solving Methods:

  • • Factoring (when possible)
  • • Quadratic formula: x = (-b ± √(b² - 4ac)) / 2a
  • • Completing the square
  • • Graphing method

Systems of Linear Equations

A system of linear equations consists of two or more linear equations with the same variables. The solution is the point(s) where all equations intersect.

Substitution Method

Solve one equation for a variable, then substitute into the other equation.

Elimination Method

Add or subtract equations to eliminate one variable, then solve.

Matrix Method

Use matrices and row operations to solve the system systematically.

Tips for Solving Equations Successfully

Check Your Work

Always substitute your solution back into the original equation to verify it's correct. This helps catch arithmetic errors and ensures accuracy.

Maintain Balance

Whatever operation you perform on one side of the equation, you must perform the same operation on the other side to maintain equality.

Work Step by Step

Break complex equations into smaller, manageable steps. This reduces errors and makes the solving process clearer and more systematic.

Watch for Special Cases

Some equations may have no solution (inconsistent) or infinite solutions (identity). Learn to recognize these special cases.

Practice Regularly

Regular practice with different types of equations builds confidence and improves problem-solving speed and accuracy.

Understand the Process

Focus on understanding why each step works rather than just memorizing procedures. This builds stronger mathematical foundation.