Solve for x if 3x^3 - 9x^2 - 12x = 0.

We need to factor the polynomial 3x^3 - 9x^2 - 12x =
0.

We notice that 3x is a common factor for all terms of
the polynimial.

Then, we will factor 3x from the
polynomial.

First, we will factor 3x from all
sides.

==> 3x( x^2 - 3x - 4) =
0

Now we will factor between
brackets.

==> 3x ( x -4)(x+ 1) =
0

To factor between brackets, we could also
use the roots formula to determine the roots of the function then obtain the
factors.

x= (-b+- sqrt(b^2 - 4ac) /
2a

==> x1= 4

==>
x2= -1

=> ( x- x1) and ( x-x2) are factor of x^2 -
3x -4.

==> x^2 - 3x - 4 = ( x-4) ( x+
1)