Approach to solve cubic inequality

Question

I would be happy to get some ideas on possible approaches to solve $$ x^3 - x^2 < 2x - 2\qquad (x \in \mathbb R). $$

Answer 1

$$x^3-x^2-2x-2<0$$

$$(x-1)(x^2-2)<0$$

$$x\in (-\infty, -\sqrt2)\cup(1,\sqrt2)$$