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