Zero Product Property

Question

Solve: x(x - 1)² = 2(x - 1)

x(x-1)²-2(x-1)=0

Answer: (x-1) (x-1) (x+1)

I can clearly see how (x-1) and (x-2) are derived.

I am not sure where the (x+1) comes from? <<<<<This is my question.

Answer 1

if you expand the equation you get:

x³-2x²-x+2 = 0

When you divide out (x-1)

(x-1)(x²-x-2) = (x-1)(x-1)(x+1)