Prove that for every real number x there exists a real numbe

Prove that for every real number x there exists a real number y so that for every real number z, yz=(x+z)^2-(x^2+z^2)

Solution

given

yz=(x+z)² - (x²+z²)

=> yz=2xz

=> yz-2xz=0

=>z(y-2x)=0

=> z=0 or y-2x=0

=>for every x there exist y