0=x^5+x^4+x^3+x^2+x+5

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Solution for 0=x^5+x^4+x^3+x^2+x+5 equation: 


Simplifying
0 = x5 + x4 + x3 + x2 + x + 5

Reorder the terms:
0 = 5 + x + x2 + x3 + x4 + x5

Solving
0 = 5 + x + x2 + x3 + x4 + x5

Solving for variable 'x'.

Combine like terms: 0 + -5 = -5
-5 + -1x + -1x2 + -1x3 + -1x4 + -1x5 = 5 + x + x2 + x3 + x4 + x5 + -5 + -1x + -1x2 + -1x3 + -1x4 + -1x5

Reorder the terms:
-5 + -1x + -1x2 + -1x3 + -1x4 + -1x5 = 5 + -5 + x + -1x + x2 + -1x2 + x3 + -1x3 + x4 + -1x4 + x5 + -1x5

Combine like terms: 5 + -5 = 0
-5 + -1x + -1x2 + -1x3 + -1x4 + -1x5 = 0 + x + -1x + x2 + -1x2 + x3 + -1x3 + x4 + -1x4 + x5 + -1x5
-5 + -1x + -1x2 + -1x3 + -1x4 + -1x5 = x + -1x + x2 + -1x2 + x3 + -1x3 + x4 + -1x4 + x5 + -1x5

Combine like terms: x + -1x = 0
-5 + -1x + -1x2 + -1x3 + -1x4 + -1x5 = 0 + x2 + -1x2 + x3 + -1x3 + x4 + -1x4 + x5 + -1x5
-5 + -1x + -1x2 + -1x3 + -1x4 + -1x5 = x2 + -1x2 + x3 + -1x3 + x4 + -1x4 + x5 + -1x5

Combine like terms: x2 + -1x2 = 0
-5 + -1x + -1x2 + -1x3 + -1x4 + -1x5 = 0 + x3 + -1x3 + x4 + -1x4 + x5 + -1x5
-5 + -1x + -1x2 + -1x3 + -1x4 + -1x5 = x3 + -1x3 + x4 + -1x4 + x5 + -1x5

Combine like terms: x3 + -1x3 = 0
-5 + -1x + -1x2 + -1x3 + -1x4 + -1x5 = 0 + x4 + -1x4 + x5 + -1x5
-5 + -1x + -1x2 + -1x3 + -1x4 + -1x5 = x4 + -1x4 + x5 + -1x5

Combine like terms: x4 + -1x4 = 0
-5 + -1x + -1x2 + -1x3 + -1x4 + -1x5 = 0 + x5 + -1x5
-5 + -1x + -1x2 + -1x3 + -1x4 + -1x5 = x5 + -1x5

Combine like terms: x5 + -1x5 = 0
-5 + -1x + -1x2 + -1x3 + -1x4 + -1x5 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + x + x2 + x3 + x4 + x5) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(5 + x + x2 + x3 + x4 + x5)' equal to zero and attempt to solve:

Simplifying
5 + x + x2 + x3 + x4 + x5 = 0

Solving
5 + x + x2 + x3 + x4 + x5 = 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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