Answer
$x=\{ 0,-1 \}$
Work Step by Step
The factored form of the given expression, $
x^3+2x^2+x=0
,$ is
\begin{align*}
x(x^2+2x+1)&=0
&\text{ (factor the $GCF=x$)}
\\
x(x+1)^2&=0
&\text{ (use $(a+b)^2=a^2+2ab+1$)}
.\end{align*}
Equating each factor to zero (Zero Product Property) results to
\begin{array}{lcl}
x=0 &\text{ OR }& (x+1)^2=0
\\&&
x+1=\pm\sqrt{0}
\text{ (take square root of both sides)}
\\&&
x+1=0
\\&&
x=-1
.\end{array}
Hence, the real solutions are $
x=\{ 0,-1 \}
$.
