9x^2-12xy-12y^2=0

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Solution for 9x^2-12xy-12y^2=0 equation:


Simplifying
9x2 + -12xy + -12y2 = 0

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

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

Solving for variable 'x'.

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

Factor a trinomial.
3((x + -2y)(3x + 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 '(3x + 2y)' equal to zero and attempt to solve: Simplifying 3x + 2y = 0 Solving 3x + 2y = 0 Move all terms containing x to the left, all other terms to the right. Add '-2y' to each side of the equation. 3x + 2y + -2y = 0 + -2y Combine like terms: 2y + -2y = 0 3x + 0 = 0 + -2y 3x = 0 + -2y Remove the zero: 3x = -2y Divide each side by '3'. x = -0.6666666667y Simplifying x = -0.6666666667y

Solution

x = {2y, -0.6666666667y}

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