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

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

A. x=0 and y=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

Correct Answer: E

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