0=30x^2y-5xy^2-10y^3

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Solution for 0=30x^2y-5xy^2-10y^3 equation: 


Simplifying
0 = 30x2y + -5xy2 + -10y3

Reorder the terms:
0 = -5xy2 + 30x2y + -10y3

Solving
0 = -5xy2 + 30x2y + -10y3

Solving for variable 'x'.
Remove the zero:
5xy2 + -30x2y + 10y3 = -5xy2 + 30x2y + -10y3 + 5xy2 + -30x2y + 10y3

Reorder the terms:
5xy2 + -30x2y + 10y3 = -5xy2 + 5xy2 + 30x2y + -30x2y + -10y3 + 10y3

Combine like terms: -5xy2 + 5xy2 = 0
5xy2 + -30x2y + 10y3 = 0 + 30x2y + -30x2y + -10y3 + 10y3
5xy2 + -30x2y + 10y3 = 30x2y + -30x2y + -10y3 + 10y3

Combine like terms: 30x2y + -30x2y = 0
5xy2 + -30x2y + 10y3 = 0 + -10y3 + 10y3
5xy2 + -30x2y + 10y3 = -10y3 + 10y3

Combine like terms: -10y3 + 10y3 = 0
5xy2 + -30x2y + 10y3 = 0

Factor out the Greatest Common Factor (GCF), '5y'.
5y(xy + -6x2 + 2y2) = 0

Factor a trinomial.
5y((-2x + -1y)(3x + -2y)) = 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 '(-2x + -1y)' equal to zero and attempt to solve:

Simplifying
-2x + -1y = 0

Solving
-2x + -1y = 0

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

Add 'y' to each side of the equation.
-2x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
-2x + 0 = 0 + y
-2x = 0 + y
Remove the zero:
-2x = y

Divide each side by '-2'.
x = -0.5y

Simplifying
x = -0.5y

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

Simplifying
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 = {-0.5y, 0.6666666667y}

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