Answer
$x= -6$, $x= 0$ or $x= 2$
Work Step by Step
Given \begin{equation}
2 x^3+8 x^2=24 x.
\end{equation} This equation can be regarded as other form of equation and can be solved by factoring.
\begin{equation}
\begin{aligned}
2 x^3+8 x^2&=24 x\\
2 x^3+8 x^2-24x&= 0\\
2x(x^2+4x-12) & =0\\
2x(x-2)(x+6)&= 0\\
\implies x&= 0\\
x&=2 \\
x&= -6.
\end{aligned}
\end{equation} The solution is $x= -6$, $x= 0$ or $x= 2$.
