(6x+6y)(2x-4y)=0

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Solution for (6x+6y)(2x-4y)=0 equation: 


Simplifying
(6x + 6y)(2x + -4y) = 0

Multiply (6x + 6y) * (2x + -4y)
(6x * (2x + -4y) + 6y * (2x + -4y)) = 0
((2x * 6x + -4y * 6x) + 6y * (2x + -4y)) = 0

Reorder the terms:
((-24xy + 12x2) + 6y * (2x + -4y)) = 0
((-24xy + 12x2) + 6y * (2x + -4y)) = 0
(-24xy + 12x2 + (2x * 6y + -4y * 6y)) = 0
(-24xy + 12x2 + (12xy + -24y2)) = 0

Reorder the terms:
(-24xy + 12xy + 12x2 + -24y2) = 0

Combine like terms: -24xy + 12xy = -12xy
(-12xy + 12x2 + -24y2) = 0

Solving
-12xy + 12x2 + -24y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(-1xy + x2 + -2y2) = 0

Factor a trinomial.
12((x + -2y)(x + y)) = 0

Ignore the factor 12.

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

Simplifying
x + -2y = 0

Solving
x + -2y = 0

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

Add '2y' to each side of the equation.
x + -2y + 2y = 0 + 2y

Combine like terms: -2y + 2y = 0
x + 0 = 0 + 2y
x = 0 + 2y
Remove the zero:
x = 2y

Simplifying
x = 2y

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 = {2y, -1y}

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