-(y-1)^2 = y-1 ..................we begin here

-(y-1) - (y-1)^2 = 0 ..........we subtract (y - 1) from both sides

-(y-1)(1+y-1) = 0 .............we factor out the common -(y - 1)

(1-y)y = 0 ........................we simplify

now since (1 -y) and y multiplied gives zero, one or the other must be zero

so 1 - y = 0 or y = 0

=> y = 1, y = 0

got it?