Answer
Solution set = $\{-6,-2\}.$
Work Step by Step
Quadratic formula: $\displaystyle \quad x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$
$x^{2}+8x+12=0 \quad\rightarrow \left\{\begin{array}{l}
a=1\\
b=8\\
c=12
\end{array}\right.$
$x=\displaystyle \frac{-8\pm\sqrt{8^{2}-4(1)(12)}}{2(1)}=\frac{-8\pm\sqrt{64-48}}{2}$
$=\displaystyle \frac{-8\pm\sqrt{16}}{2}=\frac{-8\pm 4}{2}$
$ x=\displaystyle \frac{-8-4}{2}=\frac{-12}{2}=-6\qquad$ or
$x=\displaystyle \frac{-8+4}{2}=\frac{-4}{2}=-2$
Solution set = $\{-6,-2\}.$
