Solve an equation of 3rd order

Question

What is the simplest method to solve an equation of 3rd degree.

For example: $$-x^{3} + x^{2} + x - 1 = 0$$

Please I don't want the resolution of this equation I just want the simplest method to use to solve it, then I'll try to solve it on my own.

Answer 1

$-x^{3} + x^{2} + x - 1 = 0$

$-x^{2}(x-1)+x-1=0$

$(x-1)(1-x^{2})=0$

$x=1$ and $x^{2}=1$

$x=1 , x=-1$

Answer 2

A possible method (if there's an easy first root to find : usually an integer not so far from $0$)

1. Find one root $r$ for the polynomial
2. Factor the polynomial by $(x-r)$
3. Solve the resulting 2nd degree polynomial