Answer
$0$; $3-2\ i$; $3+2 \ i$
Work Step by Step
Given \begin{equation}
t^3-6 t^2=-13 t.\end{equation} This equation can be best solved by using the quadratic formula after factoring out $t$.
\begin{equation}
\begin{aligned}
t^3-6 t^2=-13 t\\
t^3-6 t^2+13 t&=0\\
t\left(t^2-6 t+13\right)&=0\\
t& = 0\\
t^2-6 t+13&= 0\\
t&=\frac{-(-6) \pm \sqrt{(-6)^2-4 \cdot 1 \cdot 13}}{2 \cdot 1}\\
b&=\frac{6 \pm 4 i}{2 }\\
&=3\pm 2\ i.
\end{aligned}
\end{equation} The solution is \begin{equation}
t=0, \quad t=3-2\ i\ ,\quad t=3+2 \ i.
\end{equation}
