6x^3-12xy+15xy^2=0

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Solution for 6x^3-12xy+15xy^2=0 equation: 


Simplifying
6x3 + -12xy + 15xy2 = 0

Reorder the terms:
-12xy + 15xy2 + 6x3 = 0

Solving
-12xy + 15xy2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-4y + 5y2 + 2x2) = 0

Ignore the factor 3.

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-4y + 5y2 + 2x2)' equal to zero and attempt to solve:

Simplifying
-4y + 5y2 + 2x2 = 0

Reorder the terms:
2x2 + -4y + 5y2 = 0

Solving
2x2 + -4y + 5y2 = 0

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

Add '4y' to each side of the equation.
2x2 + -4y + 4y + 5y2 = 0 + 4y

Combine like terms: -4y + 4y = 0
2x2 + 0 + 5y2 = 0 + 4y
2x2 + 5y2 = 0 + 4y
Remove the zero:
2x2 + 5y2 = 4y

Add '-5y2' to each side of the equation.
2x2 + 5y2 + -5y2 = 4y + -5y2

Combine like terms: 5y2 + -5y2 = 0
2x2 + 0 = 4y + -5y2
2x2 = 4y + -5y2

Divide each side by '2'.
x2 = 2y + -2.5y2

Simplifying
x2 = 2y + -2.5y2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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