3x^3y+12x^2y^2-36xy^3=0

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Solution for 3x^3y+12x^2y^2-36xy^3=0 equation: 


Simplifying
3x3y + 12x2y2 + -36xy3 = 0

Reorder the terms:
-36xy3 + 12x2y2 + 3x3y = 0

Solving
-36xy3 + 12x2y2 + 3x3y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3xy'.
3xy(-12y2 + 4xy + x2) = 0

Factor a trinomial.
3xy((-6y + -1x)(2y + -1x)) = 0

Ignore the factor 3.

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

Simplifying
xy = 0

Solving
xy = 0

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

Simplifying
xy = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(-6y + -1x)' equal to zero and attempt to solve:

Simplifying
-6y + -1x = 0

Reorder the terms:
-1x + -6y = 0

Solving
-1x + -6y = 0

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

Add '6y' to each side of the equation.
-1x + -6y + 6y = 0 + 6y

Combine like terms: -6y + 6y = 0
-1x + 0 = 0 + 6y
-1x = 0 + 6y
Remove the zero:
-1x = 6y

Divide each side by '-1'.
x = -6y

Simplifying
x = -6y

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

Simplifying
2y + -1x = 0

Reorder the terms:
-1x + 2y = 0

Solving
-1x + 2y = 0

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

Add '-2y' to each side of the equation.
-1x + 2y + -2y = 0 + -2y

Combine like terms: 2y + -2y = 0
-1x + 0 = 0 + -2y
-1x = 0 + -2y
Remove the zero:
-1x = -2y

Divide each side by '-1'.
x = 2y

Simplifying
x = 2y
Solution
x = {-6y, 2y}

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