x+y^3=x+yx^2-xy+y^2

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Solution for x+y^3=x+yx^2-xy+y^2 equation: 


Simplifying
x + y3 = x + yx2 + -1xy + y2

Reorder the terms:
x + y3 = x + -1xy + x2y + y2

Add '-1x' to each side of the equation.
x + -1x + y3 = x + -1xy + x2y + -1x + y2

Combine like terms: x + -1x = 0
0 + y3 = x + -1xy + x2y + -1x + y2
y3 = x + -1xy + x2y + -1x + y2

Reorder the terms:
y3 = x + -1x + -1xy + x2y + y2

Combine like terms: x + -1x = 0
y3 = 0 + -1xy + x2y + y2
y3 = -1xy + x2y + y2

Solving
y3 = -1xy + x2y + y2

Solving for variable 'y'.

Reorder the terms:
xy + -1x2y + -1y2 + y3 = -1xy + x2y + y2 + xy + -1x2y + -1y2

Reorder the terms:
xy + -1x2y + -1y2 + y3 = -1xy + xy + x2y + -1x2y + y2 + -1y2

Combine like terms: -1xy + xy = 0
xy + -1x2y + -1y2 + y3 = 0 + x2y + -1x2y + y2 + -1y2
xy + -1x2y + -1y2 + y3 = x2y + -1x2y + y2 + -1y2

Combine like terms: x2y + -1x2y = 0
xy + -1x2y + -1y2 + y3 = 0 + y2 + -1y2
xy + -1x2y + -1y2 + y3 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
xy + -1x2y + -1y2 + y3 = 0

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


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

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0

Subproblem 2
Set the factor '(x + -1x2 + -1y + y2)' equal to zero and attempt to solve:

Simplifying
x + -1x2 + -1y + y2 = 0

Solving
x + -1x2 + -1y + y2 = 0

The solution to this equation could not be determined.

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

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