x^4+x^3+x^2+x+1=1

Solution for x^4+x^3+x^2+x+1=1 equation:

Simplifying
x4 + x3 + x2 + x + 1 = 1

Reorder the terms:
1 + x + x2 + x3 + x4 = 1

Add '-1' to each side of the equation.
1 + x + x2 + x3 + -1 + x4 = 1 + -1

Reorder the terms:
1 + -1 + x + x2 + x3 + x4 = 1 + -1

Combine like terms: 1 + -1 = 0
0 + x + x2 + x3 + x4 = 1 + -1
x + x2 + x3 + x4 = 1 + -1

Combine like terms: 1 + -1 = 0
x + x2 + x3 + x4 = 0

Solving
x + x2 + x3 + x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + x + x2 + x3) = 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 '(1 + x + x2 + x3)' equal to zero and attempt to solve:

Simplifying
1 + x + x2 + x3 = 0

Solving
1 + x + x2 + x3 = 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}