Solving a algebraic equation I am to solve the following equation third order equation
$x^3+x^2+x+1=0$
What I've tried so far is writing the equation as
$ x \cdot (x^2+x+1)+1=0$ 
but that didn't lead anywhere. How do I solve this without using a computer?

Factor by grouping:
$$
x^3 + x^2 + x + 1 = x^2(x+1)+(x+1) = (x+1)(x^2+1) = 0.
$$
Then $x + 1 = 0$ gives $x = -1$ and $x^2 + 1 = 0$ gives $x = \pm i$ (assuming you want to solve over the complex numbers.
