2x^3y+6x^2y^2-108xy^3=0

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Solution for 2x^3y+6x^2y^2-108xy^3=0 equation: 


Simplifying
2x3y + 6x2y2 + -108xy3 = 0

Reorder the terms:
-108xy3 + 6x2y2 + 2x3y = 0

Solving
-108xy3 + 6x2y2 + 2x3y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2xy'.
2xy(-54y2 + 3xy + x2) = 0

Factor a trinomial.
2xy((-9y + -1x)(6y + -1x)) = 0

Ignore the factor 2.

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 '(-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

Subproblem 3
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
Solution
x = {-9y, 6y}

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