Solve for $x$ : $x^4 = 5(x-1)(x^2 - x +1)$ 
Solve for $x$ : $x^4 = 5(x-1)(x^2 - x +1)$

I am having difficulty factoring the whole equation so that I can equate each factor to $0$ one by one and get the roots accordingly.

Hint: let $x=y+1$, expand, regroup and collect, then the equation becomes:
$$y^4-y^3+y^2-y+1=0$$
Multiplying by $y+1 \ne 0$ gives $y^5 + 1 = 0$ having as solutions the $5^{th}$ roots of $-1$.
