How do you find zeros of g(x)=12x^3-2x^2-2x?

You can separate one $x$ to reduce it to a second degree equation
g(x)=12x^3−2x^2−2x = x*(12x^2−2x−2)
so $g \left(x\right) = 0$ when either $x = 0$ or 12x^2−2x−2 = 0.