-3x^3y+9x^2y^2+120xy^3=0

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Solution for -3x^3y+9x^2y^2+120xy^3=0 equation: 


Simplifying
-3x3y + 9x2y2 + 120xy3 = 0

Reorder the terms:
120xy3 + 9x2y2 + -3x3y = 0

Solving
120xy3 + 9x2y2 + -3x3y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3xy'.
3xy(40y2 + 3xy + -1x2) = 0

Factor a trinomial.
3xy((8y + -1x)(5y + 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 '(8y + -1x)' equal to zero and attempt to solve:

Simplifying
8y + -1x = 0

Reorder the terms:
-1x + 8y = 0

Solving
-1x + 8y = 0

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

Add '-8y' to each side of the equation.
-1x + 8y + -8y = 0 + -8y

Combine like terms: 8y + -8y = 0
-1x + 0 = 0 + -8y
-1x = 0 + -8y
Remove the zero:
-1x = -8y

Divide each side by '-1'.
x = 8y

Simplifying
x = 8y

Subproblem 3
Set the factor '(5y + x)' equal to zero and attempt to solve:

Simplifying
5y + x = 0

Reorder the terms:
x + 5y = 0

Solving
x + 5y = 0

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

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

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

Simplifying
x = -5y
Solution
x = {8y, -5y}

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