(4x+4y)(4x+4y)=

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Solution for (4x+4y)(4x+4y)= 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 + y)(x + y)) = 0

Ignore the factor 16.

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

Simplifying
x + y = 0

Solving
x + y = 0

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

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

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

Simplifying
x = -1y

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

Simplifying
x + y = 0

Solving
x + y = 0

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

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

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

Simplifying
x = -1y
Solution
x = {-1y, -1y}

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