=x^2-5xy^2+y^3-8x^3-y^3

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Solution for =x^2-5xy^2+y^3-8x^3-y^3 equation: 


Simplifying
0 = x2 + -5xy2 + y3 + -8x3 + -1y3

Reorder the terms:
0 = -5xy2 + x2 + -8x3 + y3 + -1y3

Combine like terms: y3 + -1y3 = 0
0 = -5xy2 + x2 + -8x3 + 0
0 = -5xy2 + x2 + -8x3

Solving
0 = -5xy2 + x2 + -8x3

Solving for variable 'x'.
Remove the zero:
5xy2 + -1x2 + 8x3 = -5xy2 + x2 + -8x3 + 5xy2 + -1x2 + 8x3

Reorder the terms:
5xy2 + -1x2 + 8x3 = -5xy2 + 5xy2 + x2 + -1x2 + -8x3 + 8x3

Combine like terms: -5xy2 + 5xy2 = 0
5xy2 + -1x2 + 8x3 = 0 + x2 + -1x2 + -8x3 + 8x3
5xy2 + -1x2 + 8x3 = x2 + -1x2 + -8x3 + 8x3

Combine like terms: x2 + -1x2 = 0
5xy2 + -1x2 + 8x3 = 0 + -8x3 + 8x3
5xy2 + -1x2 + 8x3 = -8x3 + 8x3

Combine like terms: -8x3 + 8x3 = 0
5xy2 + -1x2 + 8x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(5y2 + -1x + 8x2) = 0


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 '(5y2 + -1x + 8x2)' equal to zero and attempt to solve:

Simplifying
5y2 + -1x + 8x2 = 0

Reorder the terms:
-1x + 8x2 + 5y2 = 0

Solving
-1x + 8x2 + 5y2 = 0

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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