3x^3y+18x^2y^2-81xy^3=0

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Solution for 3x^3y+18x^2y^2-81xy^3=0 equation: 


Simplifying
3x3y + 18x2y2 + -81xy3 = 0

Reorder the terms:
-81xy3 + 18x2y2 + 3x3y = 0

Solving
-81xy3 + 18x2y2 + 3x3y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3xy'.
3xy(-27y2 + 6xy + x2) = 0

Factor a trinomial.
3xy((-9y + -1x)(3y + -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 '(-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 '(3y + -1x)' equal to zero and attempt to solve:

Simplifying
3y + -1x = 0

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

Solving
-1x + 3y = 0

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

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

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

Divide each side by '-1'.
x = 3y

Simplifying
x = 3y
Solution
x = {-9y, 3y}

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