Solving Quadratic Equations by Factoring

Add 5x to both sides.

Step 2 Factor the polynomial.

The coefficient of x² is 1, so find two numbers whose product is -14 and whose sum is 5.

Step 3 Use the Zero Product Property.

Step 4 Solve the resulting equations.

Step 5 Check each answer.

x - 2 = 0

x = 2

or x + 7 = 0

or x = -7

Subtact 20 from both sides.

Step 2 Factor the polynomial.

The coefficient of x² is not 1, so find two numbers whose product is ac and whose sum is b.

ac = 6(-20) = -120 , b = 7

The two numbers are -8 and 15.

Factor 2x from the first pair of terms.

Factor 5 from the second pair of terms.

Factor out the common binomial factor, 3x - 4.

Step 3 Use the Zero Product Property.

Step 4 Solve the resulting equations.

Step 5 Check each answer.

We leave the check to you.

2x(3x - 4) + 5(3x - 4)

(3x - 4)(2x + 5)

 3x - 4 = 0 or 2x + 5

= 0

= 0

= 0