x(x-6)(x-9)=p(x)

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Solution for x(x-6)(x-9)=p(x) equation: 


Simplifying
x(x + -6)(x + -9) = p(x)

Reorder the terms:
x(-6 + x)(x + -9) = p(x)

Reorder the terms:
x(-6 + x)(-9 + x) = p(x)

Multiply (-6 + x) * (-9 + x)
x(-6(-9 + x) + x(-9 + x)) = p(x)
x((-9 * -6 + x * -6) + x(-9 + x)) = p(x)
x((54 + -6x) + x(-9 + x)) = p(x)
x(54 + -6x + (-9 * x + x * x)) = p(x)
x(54 + -6x + (-9x + x2)) = p(x)

Combine like terms: -6x + -9x = -15x
x(54 + -15x + x2) = p(x)
(54 * x + -15x * x + x2 * x) = p(x)
(54x + -15x2 + x3) = p(x)

Multiply p * x
54x + -15x2 + x3 = px

Solving
54x + -15x2 + x3 = px

Solving for variable 'x'.

Reorder the terms:
-1px + 54x + -15x2 + x3 = px + -1px

Combine like terms: px + -1px = 0
-1px + 54x + -15x2 + x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1p + 54 + -15x + x2) = 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 '(-1p + 54 + -15x + x2)' equal to zero and attempt to solve:

Simplifying
-1p + 54 + -15x + x2 = 0

Reorder the terms:
54 + -1p + -15x + x2 = 0

Solving
54 + -1p + -15x + x2 = 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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