Answer
$x=0,x=-3$ and $x=6$
Work Step by Step
The given equation is
$\Rightarrow 3x^3-9x^2-54x=0$
Factor out $3x$.
$\Rightarrow 3x(x^2-3x-18)=0$
Rewrite $-3x$ as $3x-6x$.
$\Rightarrow 3x(x^2+3x-6x-18)=0$
Group the terms.
$\Rightarrow 3x[(x^2+3x)+(-6x-18)]=0$
Factor each group.
$\Rightarrow 3x[x(x+3)-6(x+3)]=0$
Factor out $(x+3)$.
$\Rightarrow 3x(x+3)(x-6)=0$
Use zero product property.
$\Rightarrow 3x=0$ or $x+3=0$ or $x-6=0$
Solve for $x$.
$\Rightarrow x=0$ or $x=-3$ or $x=6$
Hence, the solutions are $x=0,x=-3$ and $x=6$.
