(4x-4y)(4x-4y)=0

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Solution for (4x-4y)(4x-4y)=0 equation: 


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

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

Reorder the terms:
((-16xy + 16x2) + -4y * (4x + -4y)) = 0
((-16xy + 16x2) + -4y * (4x + -4y)) = 0
(-16xy + 16x2 + (4x * -4y + -4y * -4y)) = 0
(-16xy + 16x2 + (-16xy + 16y2)) = 0

Reorder the terms:
(-16xy + -16xy + 16x2 + 16y2) = 0

Combine like terms: -16xy + -16xy = -32xy
(-32xy + 16x2 + 16y2) = 0

Solving
-32xy + 16x2 + 16y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '16'.
16(-2xy + x2 + y2) = 0

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

Ignore the factor 16.

Subproblem 1
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

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}

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