Answer
$x=-2$ or $x=2$ or $x=-\dfrac{5}{2}$
Work Step by Step
Factor the polynomial by grouping to obtain:
\begin{align*}
(2x^3+5x^2)+(-8x-20)&=0\\
x^2(2x+5)+(-4)(2x+5)&=0\\
(2x+5)(x^2-4)&=0\\
(2x+5)(x-2)(x+2)&=0
\end{align*}
Solve the equation above using the Zero-Product Property by equating each factor to zero, then solve each equation to obtain:
\begin{align*}
2x+5&=0 &\text{or}& &x-2=0& &\text{or}& &x+2=0\\\\
2x&=-5 &\text{or}& &x=2& &\text{or}& &x=-2\\\\
x&=-\frac{5}{2}
\end{align*}
