Solving Quadratic Equations by Factoring

This page demonstrates multiple examples of solving quadratic equations through factoring, following a structured approach for each problem.

Definition: The zero-product property states that if a∙b=0, then either a=0 or b=0.

Example: In solving 2x²=-3x:

1. Rearrange to 2x²+3x=0
2. Factor out x(2x+3)=0
3. Solve to get x=0 or x=-3/2

Highlight: Always start by moving all terms to one side of the equation to equal zero before attempting to factor.

Example: For 9x²=30x-25:

1. Rearrange to 9x²-30x+25=0
2. Factor to (3x-5)(3x-5)=0
3. Solve to get x=5/3

Example: For x²+7x=18:

1. Rearrange to x²+7x-18=0
2. Factor to (x+9)(x-2)=0
3. Solve to get x=-9 or x=2

Vocabulary: Greatest Common Factor (GCF) - the largest factor that divides all terms in an expression.

The page concludes with additional examples including (x-3)(x+8)=-30 and 3x²=15+4x, demonstrating various factoring scenarios and solution methods.