P(x)=x^4-3x^3-53x^2-9x

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Solution for P(x)=x^4-3x^3-53x^2-9x equation: 


Simplifying
P(x) = x4 + -3x3 + -53x2 + -9x

Multiply P * x
xP = x4 + -3x3 + -53x2 + -9x

Reorder the terms:
xP = -9x + -53x2 + -3x3 + x4

Solving
xP = -9x + -53x2 + -3x3 + x4

Solving for variable 'x'.

Reorder the terms:
9x + xP + 53x2 + 3x3 + -1x4 = -9x + -53x2 + -3x3 + x4 + 9x + 53x2 + 3x3 + -1x4

Reorder the terms:
9x + xP + 53x2 + 3x3 + -1x4 = -9x + 9x + -53x2 + 53x2 + -3x3 + 3x3 + x4 + -1x4

Combine like terms: -9x + 9x = 0
9x + xP + 53x2 + 3x3 + -1x4 = 0 + -53x2 + 53x2 + -3x3 + 3x3 + x4 + -1x4
9x + xP + 53x2 + 3x3 + -1x4 = -53x2 + 53x2 + -3x3 + 3x3 + x4 + -1x4

Combine like terms: -53x2 + 53x2 = 0
9x + xP + 53x2 + 3x3 + -1x4 = 0 + -3x3 + 3x3 + x4 + -1x4
9x + xP + 53x2 + 3x3 + -1x4 = -3x3 + 3x3 + x4 + -1x4

Combine like terms: -3x3 + 3x3 = 0
9x + xP + 53x2 + 3x3 + -1x4 = 0 + x4 + -1x4
9x + xP + 53x2 + 3x3 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
9x + xP + 53x2 + 3x3 + -1x4 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(9 + P + 53x + 3x2 + -1x3) = 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 '(9 + P + 53x + 3x2 + -1x3)' equal to zero and attempt to solve:

Simplifying
9 + P + 53x + 3x2 + -1x3 = 0

Solving
9 + P + 53x + 3x2 + -1x3 = 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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