P(x)=x(x+1)(x-2)(x-4)

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Solution for P(x)=x(x+1)(x-2)(x-4) equation: 


Simplifying
P(x) = x(x + 1)(x + -2)(x + -4)

Multiply P * x
xP = x(x + 1)(x + -2)(x + -4)

Reorder the terms:
xP = x(1 + x)(x + -2)(x + -4)

Reorder the terms:
xP = x(1 + x)(-2 + x)(x + -4)

Reorder the terms:
xP = x(1 + x)(-2 + x)(-4 + x)

Multiply (1 + x) * (-2 + x)
xP = x(1(-2 + x) + x(-2 + x))(-4 + x)
xP = x((-2 * 1 + x * 1) + x(-2 + x))(-4 + x)
xP = x((-2 + 1x) + x(-2 + x))(-4 + x)
xP = x(-2 + 1x + (-2 * x + x * x))(-4 + x)
xP = x(-2 + 1x + (-2x + x2))(-4 + x)

Combine like terms: 1x + -2x = -1x
xP = x(-2 + -1x + x2)(-4 + x)

Multiply (-2 + -1x + x2) * (-4 + x)
xP = x(-2(-4 + x) + -1x * (-4 + x) + x2(-4 + x))
xP = x((-4 * -2 + x * -2) + -1x * (-4 + x) + x2(-4 + x))
xP = x((8 + -2x) + -1x * (-4 + x) + x2(-4 + x))
xP = x(8 + -2x + (-4 * -1x + x * -1x) + x2(-4 + x))
xP = x(8 + -2x + (4x + -1x2) + x2(-4 + x))
xP = x(8 + -2x + 4x + -1x2 + (-4 * x2 + x * x2))
xP = x(8 + -2x + 4x + -1x2 + (-4x2 + x3))

Combine like terms: -2x + 4x = 2x
xP = x(8 + 2x + -1x2 + -4x2 + x3)

Combine like terms: -1x2 + -4x2 = -5x2
xP = x(8 + 2x + -5x2 + x3)
xP = (8 * x + 2x * x + -5x2 * x + x3 * x)
xP = (8x + 2x2 + -5x3 + x4)

Solving
xP = 8x + 2x2 + -5x3 + x4

Solving for variable 'x'.

Reorder the terms:
-8x + xP + -2x2 + 5x3 + -1x4 = 8x + 2x2 + -5x3 + x4 + -8x + -2x2 + 5x3 + -1x4

Reorder the terms:
-8x + xP + -2x2 + 5x3 + -1x4 = 8x + -8x + 2x2 + -2x2 + -5x3 + 5x3 + x4 + -1x4

Combine like terms: 8x + -8x = 0
-8x + xP + -2x2 + 5x3 + -1x4 = 0 + 2x2 + -2x2 + -5x3 + 5x3 + x4 + -1x4
-8x + xP + -2x2 + 5x3 + -1x4 = 2x2 + -2x2 + -5x3 + 5x3 + x4 + -1x4

Combine like terms: 2x2 + -2x2 = 0
-8x + xP + -2x2 + 5x3 + -1x4 = 0 + -5x3 + 5x3 + x4 + -1x4
-8x + xP + -2x2 + 5x3 + -1x4 = -5x3 + 5x3 + x4 + -1x4

Combine like terms: -5x3 + 5x3 = 0
-8x + xP + -2x2 + 5x3 + -1x4 = 0 + x4 + -1x4
-8x + xP + -2x2 + 5x3 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
-8x + xP + -2x2 + 5x3 + -1x4 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-8 + P + -2x + 5x2 + -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 '(-8 + P + -2x + 5x2 + -1x3)' equal to zero and attempt to solve:

Simplifying
-8 + P + -2x + 5x2 + -1x3 = 0

Solving
-8 + P + -2x + 5x2 + -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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