Answer:
-1, 0, 2
Step-by-step explanation:
[tex]\text{The zeros is for}\ f(x)=0.\\\\f(x)=3x^3-3x^2-6x\\\\f(x)=0\iff3x^3-3x^2-6x=0\qquad\text{divide both sides by 3}\\\\x^3-x^2-2x=0\qquad\text{distributive}\\\\x(x^2-x-2)=0\\\\x(x^2+x-2x-2)=0\\\\x\bigg(x(x+1)-2(x+1)\bigg)=0\\\\x(x+1)(x-2)=0\\\\\text{The product is equal to 0, when one of the factors is equal to 0.}\\\text{Therefore:}[/tex]
[tex]x(x+1)(x-2)=0\iff x=0\ \vee\ x+1=0\ \vee\ x-2=0\\\\x=0\ \vee\ x=-1\ \vee\ x=2[/tex]
