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

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


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

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

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

Solving for variable 'x'.
Remove the zero:
42xy3 + 51x2y2 + -18x3y = -42xy3 + -51x2y2 + 18x3y + 42xy3 + 51x2y2 + -18x3y

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

Combine like terms: -42xy3 + 42xy3 = 0
42xy3 + 51x2y2 + -18x3y = 0 + -51x2y2 + 51x2y2 + 18x3y + -18x3y
42xy3 + 51x2y2 + -18x3y = -51x2y2 + 51x2y2 + 18x3y + -18x3y

Combine like terms: -51x2y2 + 51x2y2 = 0
42xy3 + 51x2y2 + -18x3y = 0 + 18x3y + -18x3y
42xy3 + 51x2y2 + -18x3y = 18x3y + -18x3y

Combine like terms: 18x3y + -18x3y = 0
42xy3 + 51x2y2 + -18x3y = 0

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

Factor a trinomial.
3xy((7y + -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 '(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

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 = {3.5y, -0.6666666667y}

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