6x^3y-x^2y^2-xy^3=0

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Solution for 6x^3y-x^2y^2-xy^3=0 equation: 


Simplifying
6x3y + -1x2y2 + -1xy3 = 0

Reorder the terms:
-1xy3 + -1x2y2 + 6x3y = 0

Solving
-1xy3 + -1x2y2 + 6x3y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'xy'.
xy(-1y2 + -1xy + 6x2) = 0

Factor a trinomial.
xy((-1y + -3x)(y + -2x)) = 0


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

Simplifying
-1y + -3x = 0

Reorder the terms:
-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 '(y + -2x)' equal to zero and attempt to solve:

Simplifying
y + -2x = 0

Reorder the terms:
-2x + y = 0

Solving
-2x + y = 0

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

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

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

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

Simplifying
x = 0.5y
Solution
x = {-0.3333333333y, 0.5y}

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