Answer
$n=\{ -2,0 \}$
Work Step by Step
Isolating all the terms on the left side and then using the $GCF=
n
,$ the factored form of the given expression, $
n^2=-2n
,$ is
\begin{array}{l}\require{cancel}
n^2+2n=0
\\\\
n(n+2)=0
.\end{array}
Equating each factor to zero, wo obtain:
\begin{array}{l}\require{cancel}
n=0
,\\\\\text{OR}\\\\
n+2=0
\\\\
n=-2
.\end{array}
Hence, the solution set is $
n=\{ -2,0 \}
.$
