120x^2y-55xy^2+5y^3=0

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Solution for 120x^2y-55xy^2+5y^3=0 equation: 


Simplifying
120x2y + -55xy2 + 5y3 = 0

Reorder the terms:
-55xy2 + 120x2y + 5y3 = 0

Solving
-55xy2 + 120x2y + 5y3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5y'.
5y(-11xy + 24x2 + y2) = 0

Factor a trinomial.
5y((3x + -1y)(8x + -1y)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Add '-1y' to each side of the equation.
y + -1y = 0 + -1y
Remove the zero:
0 = -1y

Simplifying
0 = -1y

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 '(3x + -1y)' equal to zero and attempt to solve:

Simplifying
3x + -1y = 0

Solving
3x + -1y = 0

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

Add 'y' to each side of the equation.
3x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
3x + 0 = 0 + y
3x = 0 + y
Remove the zero:
3x = y

Divide each side by '3'.
x = 0.3333333333y

Simplifying
x = 0.3333333333y

Subproblem 3
Set the factor '(8x + -1y)' equal to zero and attempt to solve:

Simplifying
8x + -1y = 0

Solving
8x + -1y = 0

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

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

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

Divide each side by '8'.
x = 0.125y

Simplifying
x = 0.125y
Solution
x = {0.3333333333y, 0.125y}

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