## Elementary Algebra

$n=\{ -2,0 \}$
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 $n=\{ -2,0 \} .$