(x^5+y^5)(x^5-y^5)=0

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Solution for (x^5+y^5)(x^5-y^5)=0 equation: 


Simplifying
(x5 + y5)(x5 + -1y5) = 0

Multiply (x5 + y5) * (x5 + -1y5)
(x5(x5 + -1y5) + y5(x5 + -1y5)) = 0
((x5 * x5 + -1y5 * x5) + y5(x5 + -1y5)) = 0

Reorder the terms:
((-1x5y5 + x10) + y5(x5 + -1y5)) = 0
((-1x5y5 + x10) + y5(x5 + -1y5)) = 0
(-1x5y5 + x10 + (x5 * y5 + -1y5 * y5)) = 0
(-1x5y5 + x10 + (x5y5 + -1y10)) = 0

Reorder the terms:
(-1x5y5 + x5y5 + x10 + -1y10) = 0

Combine like terms: -1x5y5 + x5y5 = 0
(0 + x10 + -1y10) = 0
(x10 + -1y10) = 0

Solving
x10 + -1y10 = 0

Solving for variable 'x'.

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

Add 'y10' to each side of the equation.
x10 + -1y10 + y10 = 0 + y10

Combine like terms: -1y10 + y10 = 0
x10 + 0 = 0 + y10
x10 = 0 + y10
Remove the zero:
x10 = y10

Simplifying
x10 = y10

Combine like terms: y10 + -1y10 = 0
x10 + -1y10 = 0

Factor a difference between two squares.
(x5 + y5)(x5 + -1y5) = 0


Subproblem 1
Set the factor '(x5 + y5)' equal to zero and attempt to solve:

Simplifying
x5 + y5 = 0

Solving
x5 + y5 = 0

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

Add '-1y5' to each side of the equation.
x5 + y5 + -1y5 = 0 + -1y5

Combine like terms: y5 + -1y5 = 0
x5 + 0 = 0 + -1y5
x5 = 0 + -1y5
Remove the zero:
x5 = -1y5

Simplifying
x5 = -1y5

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 '(x5 + -1y5)' equal to zero and attempt to solve:

Simplifying
x5 + -1y5 = 0

Solving
x5 + -1y5 = 0

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

Add 'y5' to each side of the equation.
x5 + -1y5 + y5 = 0 + y5

Combine like terms: -1y5 + y5 = 0
x5 + 0 = 0 + y5
x5 = 0 + y5
Remove the zero:
x5 = y5

Simplifying
x5 = y5

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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