Answer
$x=\{ -2,6 \}$
Work Step by Step
Using the properties of equality, the given expression, $
x^2=4x+12
,$ is equivalent to
\begin{align*}
x^2-4x-12=0
.\end{align*}
The factored form of the expression above is
\begin{align*}
(x-6)(x+2)&=0
.\end{align*}
Equating each factor to zero (Zero Product Property), then
\begin{align*}
x-6&=0
\\\\\text{ OR }\\\\
x+2&=0
.\end{align*}
Solving each of the equations above results to
\begin{align*}
x-6&=0
\\
x&=6
\\\\\text{ OR }\\\\
x+2&=0
\\
x&=-2
.\end{align*}
Hence, the solutions are $
x=\{ -2,6 \}
.$