Why It's E?! Please Explain.

Hi all!

I need help understanding this question and its answer:

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 is E, but why? (my first choice was A)

Thanks,
Haitham