(x+y)(y-x)=

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

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

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

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

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

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

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

Solving
-1x2 + 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.
-1x2 + y2 + -1y2 = 0 + -1y2

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

Divide each side by '-1'.
x2 = y2

Simplifying
x2 = y2

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