Answer
$y=\left\{ -4,-3,3 \right\}$
Work Step by Step
The factored form of the given expression, $
y^3+4y^2=9y+36
$, is
\begin{array}{l}
y^3+4y^2-9y-36=0
\\\\
(y^3+4y^2)-(9y+36)=0
\\\\
y^2(y+4)-9(y+4)=0
\\\\
(y+4)(y^2-9)=0
\\\\
(y+4)(y+3)(y-3)=0
.\end{array}
Equating each factor to zero, then
\begin{array}{l}
y+4=0
\\
y=0-4
\\
y=-4
,\text{ OR}\\\\
y+3=0
\\
y=0-3
\\
y=-3
,\text{ OR}\\\\
y-3=0
\\
y=0+3
\\
y=3
\end{array}
Hence, $
y=\left\{ -4,-3,3 \right\}
$.
