18x^3y+57x^2y^2+30xy^3=0

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Solution for 18x^3y+57x^2y^2+30xy^3=0 equation: 


Simplifying
18x3y + 57x2y2 + 30xy3 = 0

Reorder the terms:
30xy3 + 57x2y2 + 18x3y = 0

Solving
30xy3 + 57x2y2 + 18x3y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3xy'.
3xy(10y2 + 19xy + 6x2) = 0

Factor a trinomial.
3xy((5y + 2x)(2y + 3x)) = 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 '(5y + 2x)' equal to zero and attempt to solve:

Simplifying
5y + 2x = 0

Reorder the terms:
2x + 5y = 0

Solving
2x + 5y = 0

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

Add '-5y' to each side of the equation.
2x + 5y + -5y = 0 + -5y

Combine like terms: 5y + -5y = 0
2x + 0 = 0 + -5y
2x = 0 + -5y
Remove the zero:
2x = -5y

Divide each side by '2'.
x = -2.5y

Simplifying
x = -2.5y

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

Simplifying
2y + 3x = 0

Reorder the terms:
3x + 2y = 0

Solving
3x + 2y = 0

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

Add '-2y' to each side of the equation.
3x + 2y + -2y = 0 + -2y

Combine like terms: 2y + -2y = 0
3x + 0 = 0 + -2y
3x = 0 + -2y
Remove the zero:
3x = -2y

Divide each side by '3'.
x = -0.6666666667y

Simplifying
x = -0.6666666667y
Solution
x = {-2.5y, -0.6666666667y}

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