P(x)=x^5-5x^4+5x^3+15x^3

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Solution for P(x)=x^5-5x^4+5x^3+15x^3 equation: 


Simplifying
P(x) = x5 + -5x4 + 5x3 + 15x3

Multiply P * x
xP = x5 + -5x4 + 5x3 + 15x3

Reorder the terms:
xP = 5x3 + 15x3 + -5x4 + x5

Combine like terms: 5x3 + 15x3 = 20x3
xP = 20x3 + -5x4 + x5

Solving
xP = 20x3 + -5x4 + x5

Solving for variable 'x'.

Reorder the terms:
xP + -20x3 + 5x4 + -1x5 = 20x3 + -20x3 + -5x4 + 5x4 + x5 + -1x5

Combine like terms: 20x3 + -20x3 = 0
xP + -20x3 + 5x4 + -1x5 = 0 + -5x4 + 5x4 + x5 + -1x5
xP + -20x3 + 5x4 + -1x5 = -5x4 + 5x4 + x5 + -1x5

Combine like terms: -5x4 + 5x4 = 0
xP + -20x3 + 5x4 + -1x5 = 0 + x5 + -1x5
xP + -20x3 + 5x4 + -1x5 = x5 + -1x5

Combine like terms: x5 + -1x5 = 0
xP + -20x3 + 5x4 + -1x5 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(P + -20x2 + 5x3 + -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 '(P + -20x2 + 5x3 + -1x4)' equal to zero and attempt to solve:

Simplifying
P + -20x2 + 5x3 + -1x4 = 0

Solving
P + -20x2 + 5x3 + -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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