xn+yn=2n

Solution for xn+yn=2n equation:

Simplifying
xn + yn = 2n

Solving
nx + ny = 2n

Solving for variable 'n'.

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

Add '-2n' to each side of the equation.
nx + -2n + ny = 2n + -2n

Reorder the terms:
-2n + nx + ny = 2n + -2n

Combine like terms: 2n + -2n = 0
-2n + nx + ny = 0

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

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

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0
Subproblem 2
Set the factor '(-2 + x + y)' equal to zero and attempt to solve:

Simplifying
-2 + x + y = 0

Solving
-2 + x + y = 0

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

Add '2' to each side of the equation.
-2 + x + 2 + y = 0 + 2

Reorder the terms:
-2 + 2 + x + y = 0 + 2

Combine like terms: -2 + 2 = 0
0 + x + y = 0 + 2
x + y = 0 + 2

Combine like terms: 0 + 2 = 2
x + y = 2

Add '-1x' to each side of the equation.
x + -1x + y = 2 + -1x

Combine like terms: x + -1x = 0
0 + y = 2 + -1x
y = 2 + -1x

Add '-1y' to each side of the equation.
y + -1y = 2 + -1x + -1y

Combine like terms: y + -1y = 0
0 = 2 + -1x + -1y

Simplifying
0 = 2 + -1x + -1y

The solution to this equation could not be determined.

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