Answer
$w=3$ or $w=2$ or $w=-2$
Work Step by Step
Set the equation equal to zero and use factoring.
$$
\begin{array}{r}
2 w^3-6 w^2-8 w+24=0 \\
w^3-3 w^2-4 w+12=0 \\
w^2(w-3)-4(w-3)=0 \\
(w-3)\left(w^2-4\right)=0 \\
(w-3)(w-2)(w+2)=0
\end{array}
$$
So, $w-3=0$ or $w-2=0$ or $w+2=0$ thus, $w=3$ or $w=2$ or $w=-2$.
