# Solve this? 12x^2 - 7x - 12=0

Apr 30, 2018

$x = - \frac{3}{4}$ and $x = \frac{4}{3}$

#### Explanation:

We begin by factoring the trinomial $12 {x}^{2} - 7 x - 12 = 0$

The factors of the 12 are 4 and 3.

$4 \cdot - 4 = - 16$
$3 \cdot 3 = 9$
$- 16 + 9 = 7$

$\left(4 x + 3\right) \left(3 x - 4\right) = 0$

Now set both binomial factors equal to zero and solve.

$4 x + 3 = 0$
$4 x = - 3$
$x = - \frac{3}{4}$

$3 x - 4 = 0$
$3 x = 4$
$x = \frac{4}{3}$