P(x)=5x^4-5x^3-45x^2+45x

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Solution for P(x)=5x^4-5x^3-45x^2+45x equation: 


Simplifying
P(x) = 5x4 + -5x3 + -45x2 + 45x

Multiply P * x
xP = 5x4 + -5x3 + -45x2 + 45x

Reorder the terms:
xP = 45x + -45x2 + -5x3 + 5x4

Solving
xP = 45x + -45x2 + -5x3 + 5x4

Solving for variable 'x'.

Reorder the terms:
-45x + xP + 45x2 + 5x3 + -5x4 = 45x + -45x2 + -5x3 + 5x4 + -45x + 45x2 + 5x3 + -5x4

Reorder the terms:
-45x + xP + 45x2 + 5x3 + -5x4 = 45x + -45x + -45x2 + 45x2 + -5x3 + 5x3 + 5x4 + -5x4

Combine like terms: 45x + -45x = 0
-45x + xP + 45x2 + 5x3 + -5x4 = 0 + -45x2 + 45x2 + -5x3 + 5x3 + 5x4 + -5x4
-45x + xP + 45x2 + 5x3 + -5x4 = -45x2 + 45x2 + -5x3 + 5x3 + 5x4 + -5x4

Combine like terms: -45x2 + 45x2 = 0
-45x + xP + 45x2 + 5x3 + -5x4 = 0 + -5x3 + 5x3 + 5x4 + -5x4
-45x + xP + 45x2 + 5x3 + -5x4 = -5x3 + 5x3 + 5x4 + -5x4

Combine like terms: -5x3 + 5x3 = 0
-45x + xP + 45x2 + 5x3 + -5x4 = 0 + 5x4 + -5x4
-45x + xP + 45x2 + 5x3 + -5x4 = 5x4 + -5x4

Combine like terms: 5x4 + -5x4 = 0
-45x + xP + 45x2 + 5x3 + -5x4 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-45 + P + 45x + 5x2 + -5x3) = 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 '(-45 + P + 45x + 5x2 + -5x3)' equal to zero and attempt to solve:

Simplifying
-45 + P + 45x + 5x2 + -5x3 = 0

Solving
-45 + P + 45x + 5x2 + -5x3 = 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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