How do we find u if 3u^3 - u^2 - 6u+ 2= 0

Given the polynomial
equation:

3u^3 - u^2 -6u + 2 =
0

First we will factor the
equation.

We will factor u^2 from the first 2
terms.

==> u^2 ( 3u - 1) - 6u + 2 =
0

Now we will factor -2 from the last two
terms.

==> u^2 ( 3u-1) -2 (3u -1) =
0

Now we will factor
(3u-1)

==> (3u-1)( u^2 -2) =
0

Now we will determine the
roots.

==> 3u-1 = 0 ==> 3u =1 ==> u=
1/3

==> (u^2-2) = 0 ==> u^2 = 2 ==> u=
+-sqrt2

Then we have three
roots.

==> u= { 1/3, sqrt2 ,
-sqrt2}