18x^3y+57x^2y^2+39xy^3=0

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Solution for 18x^3y+57x^2y^2+39xy^3=0 equation: 


Simplifying
18x3y + 57x2y2 + 39xy3 = 0

Reorder the terms:
39xy3 + 57x2y2 + 18x3y = 0

Solving
39xy3 + 57x2y2 + 18x3y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3xy'.
3xy(13y2 + 19xy + 6x2) = 0

Factor a trinomial.
3xy((13y + 6x)(y + x)) = 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 '(13y + 6x)' equal to zero and attempt to solve:

Simplifying
13y + 6x = 0

Reorder the terms:
6x + 13y = 0

Solving
6x + 13y = 0

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

Add '-13y' to each side of the equation.
6x + 13y + -13y = 0 + -13y

Combine like terms: 13y + -13y = 0
6x + 0 = 0 + -13y
6x = 0 + -13y
Remove the zero:
6x = -13y

Divide each side by '6'.
x = -2.166666667y

Simplifying
x = -2.166666667y

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

Simplifying
y + x = 0

Reorder the terms:
x + y = 0

Solving
x + y = 0

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

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

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

Simplifying
x = -1y
Solution
x = {-2.166666667y, -1y}

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