3x^2-12xy+12y^2=0

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Solution for 3x^2-12xy+12y^2=0 equation: 


Simplifying
3x2 + -12xy + 12y2 = 0

Reorder the terms:
-12xy + 3x2 + 12y2 = 0

Solving
-12xy + 3x2 + 12y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-4xy + x2 + 4y2) = 0

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

Ignore the factor 3.

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 + -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
Solution
x = {2y, 2y}

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