Answer
The solutions are $x=-7$, $x=-1$ and $x=6$
Work Step by Step
$x(x+1)^{3}-42(x+1)^{2}=0$
Take out common factor $(x+1)^{2}$:
$(x+1)^{2}[x(x+1)-42]=0$
$(x+1)^{2}(x^{2}+x-42)=0$
Factor $x^{2}+x-42$:
$(x+1)^{2}(x+7)(x-6)=0$
Set all three factors equal to $0$ and solve each individual equation for $x$:
$(x+1)^{2}=0$
$\sqrt{(x+1)^{2}}=\sqrt{0}$
$x+1=0$
$x=-1$
$x+7=0$
$x=-7$
$x-6=0$
$x=6$
The solutions are $x=-7$, $x=-1$ and $x=6$
