x(x-y)+y(x-y)=

Solution for x(x-y)+y(x-y)= equation:

Simplifying
x(x + -1y) + y(x + -1y) = 0
(x * x + -1y * x) + y(x + -1y) = 0

Reorder the terms:
(-1xy + x2) + y(x + -1y) = 0
(-1xy + x2) + y(x + -1y) = 0
-1xy + x2 + (x * y + -1y * y) = 0
-1xy + x2 + (xy + -1y2) = 0

Reorder the terms:
-1xy + xy + x2 + -1y2 = 0

Combine like terms: -1xy + xy = 0
0 + x2 + -1y2 = 0
x2 + -1y2 = 0

Solving
x2 + -1y2 = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add 'y2' to each side of the equation.
x2 + -1y2 + y2 = 0 + y2

Combine like terms: -1y2 + y2 = 0
x2 + 0 = 0 + y2
x2 = 0 + y2
Remove the zero:
x2 = y2

Simplifying
x2 = y2

Take the square root of each side:
x = {-1y, y}