Answer
$y=\left\{ -5,-1,1 \right\}$
Work Step by Step
The factored form of the given expression, $
x^3+5x^2=x+5
$, is
\begin{array}{l}
x^3+5x^2-x-5=0
\\\\
(x^3+5x^2)-(x+5)=0
\\\\
x^2(x+5)-(x+5)=0
\\\\
(x+5)(x^2-1)=0
\\\\
(x+5)(x-1)(x+1)=0
.\end{array}
Equating each factor to zero, then
\begin{array}{l}
x+5=0
\\
x=0-5
\\
x=-5
,\text{ OR}\\\\
x-1=0
\\
x=0+1
\\
x=1
,\text{ OR}\\\\
x+1=0
\\
x=0-1
\\
x=-1
\end{array}
Hence, $
y=\left\{ -5,-1,1 \right\}
$.
