8. $$ -3 x^{3}+15 x^{2}+42 x=0 $$

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Solve the equation $$ -3x^{3}+15x^{2}+42x=0 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$-3x^{3}+15x^{2}+42x=0$$
- step1: Factor the expression:
  $$-3x\left(x-7ight)\left(x+2ight)=0$$
- step2: Divide both sides:
  $$x\left(x-7ight)\left(x+2ight)=0$$
- step3: Separate into possible cases:
  $$\begin{align}&x=0\&x-7=0\&x+2=0\end{align}$$
- step4: Solve the equation:
  $$\begin{align}&x=0\&x=7\&x=-2\end{align}$$
- step5: Rewrite:
  $$x_{1}=-2,x_{2}=0,x_{3}=7$$
The solutions to the equation $$-3x^{3}+15x^{2}+42x=0$$ are $$x=-2$$, $$x=0$$, and $$x=7$$.
The solutions are $$x=-2$$, $$x=0$$, and $$x=7$$.

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