0=(x^2y+y)(2xy-y^2)

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Solution for 0=(x^2y+y)(2xy-y^2) equation: 


Simplifying
0 = (x2y + y)(2xy + -1y2)

Multiply (x2y + y) * (2xy + -1y2)
0 = (x2y(2xy + -1y2) + y(2xy + -1y2))
0 = ((2xy * x2y + -1y2 * x2y) + y(2xy + -1y2))

Reorder the terms:
0 = ((-1x2y3 + 2x3y2) + y(2xy + -1y2))
0 = ((-1x2y3 + 2x3y2) + y(2xy + -1y2))
0 = (-1x2y3 + 2x3y2 + (2xy * y + -1y2 * y))
0 = (-1x2y3 + 2x3y2 + (2xy2 + -1y3))

Reorder the terms:
0 = (2xy2 + -1x2y3 + 2x3y2 + -1y3)
0 = (2xy2 + -1x2y3 + 2x3y2 + -1y3)

Solving
0 = 2xy2 + -1x2y3 + 2x3y2 + -1y3

Solving for variable 'x'.
Remove the zero:
-2xy2 + x2y3 + -2x3y2 + y3 = 2xy2 + -1x2y3 + 2x3y2 + -1y3 + -2xy2 + x2y3 + -2x3y2 + y3

Reorder the terms:
-2xy2 + x2y3 + -2x3y2 + y3 = 2xy2 + -2xy2 + -1x2y3 + x2y3 + 2x3y2 + -2x3y2 + -1y3 + y3

Combine like terms: 2xy2 + -2xy2 = 0
-2xy2 + x2y3 + -2x3y2 + y3 = 0 + -1x2y3 + x2y3 + 2x3y2 + -2x3y2 + -1y3 + y3
-2xy2 + x2y3 + -2x3y2 + y3 = -1x2y3 + x2y3 + 2x3y2 + -2x3y2 + -1y3 + y3

Combine like terms: -1x2y3 + x2y3 = 0
-2xy2 + x2y3 + -2x3y2 + y3 = 0 + 2x3y2 + -2x3y2 + -1y3 + y3
-2xy2 + x2y3 + -2x3y2 + y3 = 2x3y2 + -2x3y2 + -1y3 + y3

Combine like terms: 2x3y2 + -2x3y2 = 0
-2xy2 + x2y3 + -2x3y2 + y3 = 0 + -1y3 + y3
-2xy2 + x2y3 + -2x3y2 + y3 = -1y3 + y3

Combine like terms: -1y3 + y3 = 0
-2xy2 + x2y3 + -2x3y2 + y3 = 0

Factor out the Greatest Common Factor (GCF), 'y2'.
y2(-2x + x2y + -2x3 + y) = 0


Subproblem 1
Set the factor 'y2' equal to zero and attempt to solve:

Simplifying
y2 = 0

Solving
y2 = 0

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

Add '-1y2' to each side of the equation.
y2 + -1y2 = 0 + -1y2
Remove the zero:
0 = -1y2

Simplifying
0 = -1y2

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 + x2y + -2x3 + y)' equal to zero and attempt to solve:

Simplifying
-2x + x2y + -2x3 + y = 0

Solving
-2x + x2y + -2x3 + y = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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