Answer
$x= -7 , $ $ x= 0$, $ x= 12$
Work Step by Step
Use factoring.$$
\begin{aligned}
3 x^3-15 x^2&=252 x \\
3 x^3-15 x^2-252 x&=0 \\
3 x\left(x^2-5 x-84\right)&=0 \\
3 x\left(x^2-12 x+7 x-84\right)&=0 \\
3 x[x(x-12)+7(x-12)]&=0 \\
3 x(x-12)(x+7)&=0.
\end{aligned}
$$ This gives: $$
\begin{aligned}
3 x & =0 \\
x & =0 \\
x-12 & =0 \\
x & =12 \\
x+7 & =0 \\
x & =-7.
\end{aligned}
$$ The solutions are: $$x= -7, x= 0, x= 12.$$ Define the following function and plot it. We see that the zeros are where they should be. $$
f(x) =3 x^3-15 x^2-252 x.
$$
