(4x-4y)(5y-5x)=

Solution for (4x-4y)(5y-5x)= equation:

Simplifying
(4x + -4y)(5y + -5x) = 0

Reorder the terms:
(4x + -4y)(-5x + 5y) = 0

Multiply (4x + -4y) * (-5x + 5y)
(4x * (-5x + 5y) + -4y * (-5x + 5y)) = 0
((-5x * 4x + 5y * 4x) + -4y * (-5x + 5y)) = 0

Reorder the terms:
((20xy + -20x2) + -4y * (-5x + 5y)) = 0
((20xy + -20x2) + -4y * (-5x + 5y)) = 0
(20xy + -20x2 + (-5x * -4y + 5y * -4y)) = 0
(20xy + -20x2 + (20xy + -20y2)) = 0

Reorder the terms:
(20xy + 20xy + -20x2 + -20y2) = 0

Combine like terms: 20xy + 20xy = 40xy
(40xy + -20x2 + -20y2) = 0

Solving
40xy + -20x2 + -20y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '20'.
20(2xy + -1x2 + -1y2) = 0

Factor a trinomial.
20((-1x + y)(x + -1y)) = 0

Ignore the factor 20.
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}