P(x)=(x-3)(x-9)(x+2)(x+0)

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Solution for P(x)=(x-3)(x-9)(x+2)(x+0) equation: 


Simplifying
P(x) = (x + -3)(x + -9)(x + 2)(x + 0)

Multiply P * x
xP = (x + -3)(x + -9)(x + 2)(x + 0)

Reorder the terms:
xP = (-3 + x)(x + -9)(x + 2)(x + 0)

Reorder the terms:
xP = (-3 + x)(-9 + x)(x + 2)(x + 0)

Reorder the terms:
xP = (-3 + x)(-9 + x)(2 + x)(x + 0)

Reorder the terms:
xP = (-3 + x)(-9 + x)(2 + x)(0 + x)
Remove the zero:
xP = (-3 + x)(-9 + x)(2 + x)(x)

Reorder the terms for easier multiplication:
xP = x(-3 + x)(-9 + x)(2 + x)

Multiply (-3 + x) * (-9 + x)
xP = x(-3(-9 + x) + x(-9 + x))(2 + x)
xP = x((-9 * -3 + x * -3) + x(-9 + x))(2 + x)
xP = x((27 + -3x) + x(-9 + x))(2 + x)
xP = x(27 + -3x + (-9 * x + x * x))(2 + x)
xP = x(27 + -3x + (-9x + x2))(2 + x)

Combine like terms: -3x + -9x = -12x
xP = x(27 + -12x + x2)(2 + x)

Multiply (27 + -12x + x2) * (2 + x)
xP = x(27(2 + x) + -12x * (2 + x) + x2(2 + x))
xP = x((2 * 27 + x * 27) + -12x * (2 + x) + x2(2 + x))
xP = x((54 + 27x) + -12x * (2 + x) + x2(2 + x))
xP = x(54 + 27x + (2 * -12x + x * -12x) + x2(2 + x))
xP = x(54 + 27x + (-24x + -12x2) + x2(2 + x))
xP = x(54 + 27x + -24x + -12x2 + (2 * x2 + x * x2))
xP = x(54 + 27x + -24x + -12x2 + (2x2 + x3))

Combine like terms: 27x + -24x = 3x
xP = x(54 + 3x + -12x2 + 2x2 + x3)

Combine like terms: -12x2 + 2x2 = -10x2
xP = x(54 + 3x + -10x2 + x3)
xP = (54 * x + 3x * x + -10x2 * x + x3 * x)
xP = (54x + 3x2 + -10x3 + x4)

Solving
xP = 54x + 3x2 + -10x3 + x4

Solving for variable 'x'.

Reorder the terms:
-54x + xP + -3x2 + 10x3 + -1x4 = 54x + 3x2 + -10x3 + x4 + -54x + -3x2 + 10x3 + -1x4

Reorder the terms:
-54x + xP + -3x2 + 10x3 + -1x4 = 54x + -54x + 3x2 + -3x2 + -10x3 + 10x3 + x4 + -1x4

Combine like terms: 54x + -54x = 0
-54x + xP + -3x2 + 10x3 + -1x4 = 0 + 3x2 + -3x2 + -10x3 + 10x3 + x4 + -1x4
-54x + xP + -3x2 + 10x3 + -1x4 = 3x2 + -3x2 + -10x3 + 10x3 + x4 + -1x4

Combine like terms: 3x2 + -3x2 = 0
-54x + xP + -3x2 + 10x3 + -1x4 = 0 + -10x3 + 10x3 + x4 + -1x4
-54x + xP + -3x2 + 10x3 + -1x4 = -10x3 + 10x3 + x4 + -1x4

Combine like terms: -10x3 + 10x3 = 0
-54x + xP + -3x2 + 10x3 + -1x4 = 0 + x4 + -1x4
-54x + xP + -3x2 + 10x3 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
-54x + xP + -3x2 + 10x3 + -1x4 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-54 + P + -3x + 10x2 + -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 '(-54 + P + -3x + 10x2 + -1x3)' equal to zero and attempt to solve:

Simplifying
-54 + P + -3x + 10x2 + -1x3 = 0

Solving
-54 + P + -3x + 10x2 + -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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