Answer
$x=\left\{ -2,-4 \right\}$
Work Step by Step
The factored form of the given equation, $
x^2+6x+8=0
,$ is
\begin{align*}
(x+2)(x+4)&=0
.\end{align*}
Equating each factor to zero (Zero Product Property), the solutions of the equation above are
\begin{align*}
x+2&=0
\\\\\text{ OR}\\\\
x+4&=0
.\end{align*}
Solving each equation above results to
\begin{align*}
x+2&=0
\\
x&=-2
\\\\\text{ OR}\\\\
x+4&=0
\\
x&=-4
.\end{align*}
Hence, the solutions are $
x=\left\{ -2, -4 \right\}
.$
