#### Answer

The solutions are $-3i, 3i,$ and $1$.

#### Work Step by Step

Group the first two terms together and the last two terms together to obtain:
$(y^3+9y)+(-y^2-9)=0$
Factor out the GCF in each group ($y$ in the first and $-1$) to obtain:
$y(y^2+9)+(-1)(y^2+9)$
Factor out the GCF of the expression ($y^2+9$) to obtain:
$=(y^2+9)[y+(-1)]
\\=(y^2+9)(y-1)$
Use the Zero Factor Property by equating each factor to zero, then solve each equation to obtain:
\begin{array}{ccc}
\\&y^2+9=0 &\text{or} &y-1=0
\\&y^2=-9 &\text{or} &y=1
\\&y=\pm\sqrt{-9} &\text{or} &y=1
\\&y=\pm 3i &\text{or} &y=1
\end{array}
Therefore, the solutions are $-3i, 3i,$ and $1$.