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

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

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

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

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

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

Combine like terms: -1xy + 1xy = 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}