2x(x-y)-y(2y-2x)=

Solution for 2x(x-y)-y(2y-2x)= equation:

Simplifying
2x(x + -1y) + -1y(2y + -2x) = 0
(x * 2x + -1y * 2x) + -1y(2y + -2x) = 0

Reorder the terms:
(-2xy + 2x2) + -1y(2y + -2x) = 0
(-2xy + 2x2) + -1y(2y + -2x) = 0

Reorder the terms:
-2xy + 2x2 + -1y(-2x + 2y) = 0
-2xy + 2x2 + (-2x * -1y + 2y * -1y) = 0
-2xy + 2x2 + (2xy + -2y2) = 0

Reorder the terms:
-2xy + 2xy + 2x2 + -2y2 = 0

Combine like terms: -2xy + 2xy = 0
0 + 2x2 + -2y2 = 0
2x2 + -2y2 = 0

Solving
2x2 + -2y2 = 0

Solving for variable 'x'.

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

Add '2y2' to each side of the equation.
2x2 + -2y2 + 2y2 = 0 + 2y2

Combine like terms: -2y2 + 2y2 = 0
2x2 + 0 = 0 + 2y2
2x2 = 0 + 2y2
Remove the zero:
2x2 = 2y2

Divide each side by '2'.
x2 = y2

Simplifying
x2 = y2

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