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 or y = 0
e. x = 1 or z = 0

The correct answer given is (e).

Do the values of x and z have to be tested seperately?