x^3+y^3=(x+y)(x^2-xy+x^2)

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


Simplifying
x3 + y3 = (x + y)(x2 + -1xy + x2)

Reorder the terms:
x3 + y3 = (x + y)(-1xy + x2 + x2)

Combine like terms: x2 + x2 = 2x2
x3 + y3 = (x + y)(-1xy + 2x2)

Multiply (x + y) * (-1xy + 2x2)
x3 + y3 = (x(-1xy + 2x2) + y(-1xy + 2x2))
x3 + y3 = ((-1xy * x + 2x2 * x) + y(-1xy + 2x2))
x3 + y3 = ((-1x2y + 2x3) + y(-1xy + 2x2))
x3 + y3 = (-1x2y + 2x3 + (-1xy * y + 2x2 * y))
x3 + y3 = (-1x2y + 2x3 + (-1xy2 + 2x2y))

Reorder the terms:
x3 + y3 = (-1xy2 + -1x2y + 2x2y + 2x3)

Combine like terms: -1x2y + 2x2y = 1x2y
x3 + y3 = (-1xy2 + 1x2y + 2x3)

Solving
x3 + y3 = -1xy2 + 1x2y + 2x3

Solving for variable 'x'.

Reorder the terms:
xy2 + -1x2y + x3 + -2x3 + y3 = -1xy2 + 1x2y + 2x3 + xy2 + -1x2y + -2x3

Combine like terms: x3 + -2x3 = -1x3
xy2 + -1x2y + -1x3 + y3 = -1xy2 + 1x2y + 2x3 + xy2 + -1x2y + -2x3

Reorder the terms:
xy2 + -1x2y + -1x3 + y3 = -1xy2 + xy2 + 1x2y + -1x2y + 2x3 + -2x3

Combine like terms: -1xy2 + xy2 = 0
xy2 + -1x2y + -1x3 + y3 = 0 + 1x2y + -1x2y + 2x3 + -2x3
xy2 + -1x2y + -1x3 + y3 = 1x2y + -1x2y + 2x3 + -2x3

Combine like terms: 1x2y + -1x2y = 0
xy2 + -1x2y + -1x3 + y3 = 0 + 2x3 + -2x3
xy2 + -1x2y + -1x3 + y3 = 2x3 + -2x3

Combine like terms: 2x3 + -2x3 = 0
xy2 + -1x2y + -1x3 + y3 = 0

The solution to this equation could not be determined.

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