[tex]f(x)=3x^3+2x^2-12x-8\\\\f(x)=0\iff3x^3+2x^2-12x-8=0\\\\x^2(3x+2)-4(3x+2)=0\\\\(3x+2)(x^2-4)=0\iff3x+2=0\ \vee\ x^2-4=0\\\\3x+2=0\qquad|-2\\\\3x=-2\qquad|:3\\\\\boxed{x=-\dfrac{2}{3}}\\\\x^2-4\qquad|+4\\\\x^2=4\to x=\pm\sqrt4\\\\\boxed{x-2}\ \vee\ \boxed{x=2}\\\\Answer:\ x=-2,\ x=-\dfrac{2}{3}\ or\ x=2.[/tex]
