Answer
$x=\left\{ -\dfrac{5}{2},-2,2 \right\}$
Work Step by Step
The factored form of the given expression, $
2x^3+5x^2=8x+20
$, is
\begin{array}{l}
2x^3+5x^2-8x-20=0
\\\\=
(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{array}
Equating each factor to zero, then
\begin{array}{l}
2x+5=0
\\
2x=0-5
\\
2x=-5
\\
x=-\dfrac{5}{2}
,\text{ OR}\\\\
x+2=0
\\
x=0-2
\\
x=-2
,\text{ OR}\\\\
x-2=0
\\
x=0+2
\\
x=2
.\end{array}
Hence, $
x=\left\{ -\dfrac{5}{2},-2,2 \right\}
$.
