(X * Y) = [(Z*X) + (Z*Y) + (Z^2)], Z =/= 0; Solve in terms of Z?

Question

Ive been out of school too long and cant remember how to answer this. As far as I can get is:

(X * Y) = [(Z*X) + (Z*Y) + (Z^2)]

XY = Z(X + Y + Z)

I just can't figure out the right move to get Z by itself.

Answer 1

This is a quadratic equation, which is, after rearranging slightly,

z² + z(x+y) - xy = 0

The solution is

z = (1/2)(-(x+y) ± √((x+y)² + 4xy)