solve for x if x^3 +x^2 +x +1 = 0

Given the equation:

x^3+ x^2
+ x +1 = 0

We need to find x values that satisfies the
equation.

First we will simplify by
factoring.

We will factor x^2 from the first two
terms.

==> x^2 ( x+1) + x+1 =
0

Now we will factor
x+1

==> (x+1)*(x^2+1) =
0

==> x+1 = 0 ==> x1=
-1

==> x^2 + 1 = 0 ==> x=
+-i

Then, there are 3 roots for the
equation.

==> x= { -1, i,
-i}