18x^3y-51x^2y^2-42xy^3=0

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Solution for 18x^3y-51x^2y^2-42xy^3=0 equation: 


Simplifying
18x3y + -51x2y2 + -42xy3 = 0

Reorder the terms:
-42xy3 + -51x2y2 + 18x3y = 0

Solving
-42xy3 + -51x2y2 + 18x3y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3xy'.
3xy(-14y2 + -17xy + 6x2) = 0

Factor a trinomial.
3xy((-2y + -3x)(7y + -2x)) = 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 '(-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

Subproblem 3
Set the factor '(7y + -2x)' equal to zero and attempt to solve:

Simplifying
7y + -2x = 0

Reorder the terms:
-2x + 7y = 0

Solving
-2x + 7y = 0

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

Add '-7y' to each side of the equation.
-2x + 7y + -7y = 0 + -7y

Combine like terms: 7y + -7y = 0
-2x + 0 = 0 + -7y
-2x = 0 + -7y
Remove the zero:
-2x = -7y

Divide each side by '-2'.
x = 3.5y

Simplifying
x = 3.5y
Solution
x = {-0.6666666667y, 3.5y}

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