To solve the quadratic equation using factoring

1. Transform the equation using standard form in which one side is zero.

2. Factor the non-zero side.

3. Set each factor to zero (Remember: a product of factors is zero if and only if one or more of the factors is zero).

4. Solve each resulting equation.

**Example 1:**

Solve the equation, *x*^{2} – 3*x* – 10 = 0

Factor the left side: (*x* – 5)(*x* + 2) = 0

Set each factor to zero: *x* – 5 = 0 or *x* + 2 = 0

Solve each equation: *x* = 5 or *x* = –2

The solution set is {5, –2}.

**Example 2:**

Solve the equation, 2*x*^{2} + 5*x* = 12

Set the right side to zero: 2*x*^{2} + 5*x* – 12 = 0

Factor the left side: (2*x* – 3)(*x* + 4) = 0

Set each factor to zero: 2*x* – 3 = 0 or *x* + 4 = 0

Solve each equation: *x* = 3/2 or *x* = –4

The solution set is {3/2, –4}