3x^2-12yx+9y^2=0

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Solution for 3x^2-12yx+9y^2=0 equation:


Simplifying
3x2 + -12yx + 9y2 = 0

Reorder the terms:
-12xy + 3x2 + 9y2 = 0

Solving
-12xy + 3x2 + 9y2 = 0

Solving for variable 'x'.

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

Factor a trinomial.
3((x + -3y)(x + -1y)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(x + -3y)' equal to zero and attempt to solve: Simplifying x + -3y = 0 Solving x + -3y = 0 Move all terms containing x to the left, all other terms to the right. Add '3y' to each side of the equation. x + -3y + 3y = 0 + 3y Combine like terms: -3y + 3y = 0 x + 0 = 0 + 3y x = 0 + 3y Remove the zero: x = 3y Simplifying x = 3y

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 = {3y, y}

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