Solving Quadratic Equations Using Factoring

To solve an 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: $x = \frac{3}{2}$ or $x = - 4$

The solution set is ${\frac{3}{2}, - 4}$ .