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

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Solution for 0=x^4+x^3+x^2+x+1 equation: 


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

Reorder the terms:
0 = 1 + x + x2 + x3 + x4

Solving
0 = 1 + x + x2 + x3 + x4

Solving for variable 'x'.

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

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

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + x + x2 + x3 + x4) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(1 + x + x2 + x3 + x4)' equal to zero and attempt to solve:

Simplifying
1 + x + x2 + x3 + x4 = 0

Solving
1 + x + x2 + x3 + x4 = 0

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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