P(x)=x^5+4x^4+6x^3+4x^2+5x

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Solution for P(x)=x^5+4x^4+6x^3+4x^2+5x equation: 


Simplifying
P(x) = x5 + 4x4 + 6x3 + 4x2 + 5x

Multiply P * x
xP = x5 + 4x4 + 6x3 + 4x2 + 5x

Reorder the terms:
xP = 5x + 4x2 + 6x3 + 4x4 + x5

Solving
xP = 5x + 4x2 + 6x3 + 4x4 + x5

Solving for variable 'x'.

Reorder the terms:
-5x + xP + -4x2 + -6x3 + -4x4 + -1x5 = 5x + 4x2 + 6x3 + 4x4 + x5 + -5x + -4x2 + -6x3 + -4x4 + -1x5

Reorder the terms:
-5x + xP + -4x2 + -6x3 + -4x4 + -1x5 = 5x + -5x + 4x2 + -4x2 + 6x3 + -6x3 + 4x4 + -4x4 + x5 + -1x5

Combine like terms: 5x + -5x = 0
-5x + xP + -4x2 + -6x3 + -4x4 + -1x5 = 0 + 4x2 + -4x2 + 6x3 + -6x3 + 4x4 + -4x4 + x5 + -1x5
-5x + xP + -4x2 + -6x3 + -4x4 + -1x5 = 4x2 + -4x2 + 6x3 + -6x3 + 4x4 + -4x4 + x5 + -1x5

Combine like terms: 4x2 + -4x2 = 0
-5x + xP + -4x2 + -6x3 + -4x4 + -1x5 = 0 + 6x3 + -6x3 + 4x4 + -4x4 + x5 + -1x5
-5x + xP + -4x2 + -6x3 + -4x4 + -1x5 = 6x3 + -6x3 + 4x4 + -4x4 + x5 + -1x5

Combine like terms: 6x3 + -6x3 = 0
-5x + xP + -4x2 + -6x3 + -4x4 + -1x5 = 0 + 4x4 + -4x4 + x5 + -1x5
-5x + xP + -4x2 + -6x3 + -4x4 + -1x5 = 4x4 + -4x4 + x5 + -1x5

Combine like terms: 4x4 + -4x4 = 0
-5x + xP + -4x2 + -6x3 + -4x4 + -1x5 = 0 + x5 + -1x5
-5x + xP + -4x2 + -6x3 + -4x4 + -1x5 = x5 + -1x5

Combine like terms: x5 + -1x5 = 0
-5x + xP + -4x2 + -6x3 + -4x4 + -1x5 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-5 + P + -4x + -6x2 + -4x3 + -1x4) = 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 '(-5 + P + -4x + -6x2 + -4x3 + -1x4)' equal to zero and attempt to solve:

Simplifying
-5 + P + -4x + -6x2 + -4x3 + -1x4 = 0

Solving
-5 + P + -4x + -6x2 + -4x3 + -1x4 = 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}

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