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

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

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

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

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

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

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

Combine like terms: x2 + x2 = 2x2
2x2 = 0

Solving
2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
x2 = 0

Simplifying
x2 = 0

Take the square root of each side:
x = {0}