Solve the following equation for x: 3x^3 + 22x^2 - 16x = 0

3x^3 + 22x^2 - 16x = 0

First
we will factor x from all terms.

==> x*(3x^2 + 22x -
16) = 0

Now we will find the roots for the quadratic
equation.

==> x1= (-22 + sqrt(484+4*3*16) /
2*3

          = (-22 + 26)/6 = ( 4/6 =
2/3

==> x1= 2/3 ==>
(3x-2) is a factor for the quadratic
equation.

==> x2= ( -22-26)/6 = -48/6 =
-8.

==> x2= -8. Then,
(x+8) is a factor of the quadratic
equation.

==> 3x^3 + 22x^2 - 16x = x*(3x^2 + 22x
-16)

                                   =
x*(3x-2)(x+8)

Then, there are three solutions to the
equation.

x1= 0 , x2= 2/3, and x3=
-8.

==> x= { -8, 0,
2/3}.