(x-y)(y-x)=

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

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

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

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

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

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

Combine like terms: xy + 1xy = 2xy
(2xy + -1x2 + -1y2) = 0

Solving
2xy + -1x2 + -1y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1x + y)(x + -1y) = 0

Subproblem 1
Set the factor '(-1x + y)' equal to zero and attempt to solve:

Simplifying
-1x + y = 0

Solving
-1x + y = 0

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

Add '-1y' to each side of the equation.
-1x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
-1x + 0 = 0 + -1y
-1x = 0 + -1y
Remove the zero:
-1x = -1y

Divide each side by '-1'.
x = y

Simplifying
x = y
Subproblem 2
Set the factor '(x + -1y)' equal to zero and attempt to solve:

Simplifying
x + -1y = 0

Solving
x + -1y = 0

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

Add 'y' to each side of the equation.
x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
x + 0 = 0 + y
x = 0 + y
Remove the zero:
x = y

Simplifying
x = y
Solution
x = {y, y}