Answer
$x=0,\quad x=5+3 i,\quad x=5-3 i$
Work Step by Step
Given \begin{equation}
2 x^3-20 x^2+68 x=0.
\end{equation} Factor out $2x$: \begin{equation}
\begin{aligned}
2 x^3-20 x^2+68 x&=0\\
2x(x^2-10 x+34) &=0\\
x&= 0\\
x^2-10 x+34&= 0.
\end{aligned}
\end{equation} Use the quadratic formula: \begin{equation}
\begin{aligned}
x & =\frac{-(-10) \pm \sqrt{(-10)^2-4 \cdot 1 \cdot 34}}{2 \cdot 1}\\
& =\frac{10\pm \sqrt{-36}}{2} \\
&= \frac{10 \pm 6 i}{2 } \\
\therefore &x= 5+3i\\
x&= 5-3i.
\end{aligned}
\end{equation} The solution is $$x=0,\quad x=5+3 i,\quad x=5-3 i.$$
