P(x)=4x(x-6)(x^2-8x+17)

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Solution for P(x)=4x(x-6)(x^2-8x+17) equation: 


Simplifying
P(x) = 4x(x + -6)(x2 + -8x + 17)

Multiply P * x
xP = 4x(x + -6)(x2 + -8x + 17)

Reorder the terms:
xP = 4x(-6 + x)(x2 + -8x + 17)

Reorder the terms:
xP = 4x(-6 + x)(17 + -8x + x2)

Multiply (-6 + x) * (17 + -8x + x2)
xP = 4x(-6(17 + -8x + x2) + x(17 + -8x + x2))
xP = 4x((17 * -6 + -8x * -6 + x2 * -6) + x(17 + -8x + x2))
xP = 4x((-102 + 48x + -6x2) + x(17 + -8x + x2))
xP = 4x(-102 + 48x + -6x2 + (17 * x + -8x * x + x2 * x))
xP = 4x(-102 + 48x + -6x2 + (17x + -8x2 + x3))

Reorder the terms:
xP = 4x(-102 + 48x + 17x + -6x2 + -8x2 + x3)

Combine like terms: 48x + 17x = 65x
xP = 4x(-102 + 65x + -6x2 + -8x2 + x3)

Combine like terms: -6x2 + -8x2 = -14x2
xP = 4x(-102 + 65x + -14x2 + x3)
xP = (-102 * 4x + 65x * 4x + -14x2 * 4x + x3 * 4x)
xP = (-408x + 260x2 + -56x3 + 4x4)

Solving
xP = -408x + 260x2 + -56x3 + 4x4

Solving for variable 'x'.

Reorder the terms:
408x + xP + -260x2 + 56x3 + -4x4 = -408x + 260x2 + -56x3 + 4x4 + 408x + -260x2 + 56x3 + -4x4

Reorder the terms:
408x + xP + -260x2 + 56x3 + -4x4 = -408x + 408x + 260x2 + -260x2 + -56x3 + 56x3 + 4x4 + -4x4

Combine like terms: -408x + 408x = 0
408x + xP + -260x2 + 56x3 + -4x4 = 0 + 260x2 + -260x2 + -56x3 + 56x3 + 4x4 + -4x4
408x + xP + -260x2 + 56x3 + -4x4 = 260x2 + -260x2 + -56x3 + 56x3 + 4x4 + -4x4

Combine like terms: 260x2 + -260x2 = 0
408x + xP + -260x2 + 56x3 + -4x4 = 0 + -56x3 + 56x3 + 4x4 + -4x4
408x + xP + -260x2 + 56x3 + -4x4 = -56x3 + 56x3 + 4x4 + -4x4

Combine like terms: -56x3 + 56x3 = 0
408x + xP + -260x2 + 56x3 + -4x4 = 0 + 4x4 + -4x4
408x + xP + -260x2 + 56x3 + -4x4 = 4x4 + -4x4

Combine like terms: 4x4 + -4x4 = 0
408x + xP + -260x2 + 56x3 + -4x4 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(408 + P + -260x + 56x2 + -4x3) = 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 '(408 + P + -260x + 56x2 + -4x3)' equal to zero and attempt to solve:

Simplifying
408 + P + -260x + 56x2 + -4x3 = 0

Solving
408 + P + -260x + 56x2 + -4x3 = 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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