Can anybody tell me how to solve this;

If xy + z = x(y + z), which of the following must be true?

a) x = 0 and z = 0
b) x = 1 and y = 1
c) y = 1 and z = 0
d) x = 1 and y =0
e) x = 1 and z = 0

The answer is E, I solved for x and got one, however, I'm uncertain on how the answer is z = 0 and not y = 0