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

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

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

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

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

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

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

Solving
x2 + y2 = 0

Solving for variable 'x'.

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

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

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

Simplifying
x2 = -1y2

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

The solution to this equation could not be determined.