xn+yn+zn=wn

Solution for xn+yn+zn=wn equation:

Simplifying
xn + yn + zn = wn

Solving
nx + ny + nz = nw

Solving for variable 'n'.

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

Add '-1nw' to each side of the equation.
nx + ny + -1nw + nz = nw + -1nw

Reorder the terms:
-1nw + nx + ny + nz = nw + -1nw

Combine like terms: nw + -1nw = 0
-1nw + nx + ny + nz = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-1w + x + y + z) = 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 '(-1w + x + y + z)' equal to zero and attempt to solve:

Simplifying
-1w + x + y + z = 0

Solving
-1w + x + y + z = 0

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

Add 'w' to each side of the equation.
-1w + x + y + w + z = 0 + w

Reorder the terms:
-1w + w + x + y + z = 0 + w

Combine like terms: -1w + w = 0
0 + x + y + z = 0 + w
x + y + z = 0 + w
Remove the zero:
x + y + z = w

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

Reorder the terms:
x + -1x + y + z = w + -1x

Combine like terms: x + -1x = 0
0 + y + z = w + -1x
y + z = w + -1x

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

Combine like terms: y + -1y = 0
0 + z = w + -1x + -1y
z = w + -1x + -1y

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

Combine like terms: z + -1z = 0
0 = w + -1x + -1y + -1z

Simplifying
0 = w + -1x + -1y + -1z

The solution to this equation could not be determined.

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