12x^4-104x^3y-36y^2x^2=0

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Solution for 12x^4-104x^3y-36y^2x^2=0 equation: 


Simplifying
12x4 + -104x3y + -36y2x2 = 0

Reorder the terms:
-36x2y2 + -104x3y + 12x4 = 0

Solving
-36x2y2 + -104x3y + 12x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x2'.
4x2(-9y2 + -26xy + 3x2) = 0

Factor a trinomial.
4x2((-1y + -3x)(9y + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

Subproblem 2
Set the factor '(-1y + -3x)' equal to zero and attempt to solve:

Simplifying
-1y + -3x = 0

Reorder the terms:
-3x + -1y = 0

Solving
-3x + -1y = 0

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

Add 'y' to each side of the equation.
-3x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
-3x + 0 = 0 + y
-3x = 0 + y
Remove the zero:
-3x = y

Divide each side by '-3'.
x = -0.3333333333y

Simplifying
x = -0.3333333333y

Subproblem 3
Set the factor '(9y + -1x)' equal to zero and attempt to solve:

Simplifying
9y + -1x = 0

Reorder the terms:
-1x + 9y = 0

Solving
-1x + 9y = 0

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

Add '-9y' to each side of the equation.
-1x + 9y + -9y = 0 + -9y

Combine like terms: 9y + -9y = 0
-1x + 0 = 0 + -9y
-1x = 0 + -9y
Remove the zero:
-1x = -9y

Divide each side by '-1'.
x = 9y

Simplifying
x = 9y
Solution
x = {0, -0.3333333333y, 9y}

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