x^3+27+(x+3)(x-9)=0

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Solution for x^3+27+(x+3)(x-9)=0 equation: 


Simplifying
x3 + 27 + (x + 3)(x + -9) = 0

Reorder the terms:
x3 + 27 + (3 + x)(x + -9) = 0

Reorder the terms:
x3 + 27 + (3 + x)(-9 + x) = 0

Multiply (3 + x) * (-9 + x)
x3 + 27 + (3(-9 + x) + x(-9 + x)) = 0
x3 + 27 + ((-9 * 3 + x * 3) + x(-9 + x)) = 0
x3 + 27 + ((-27 + 3x) + x(-9 + x)) = 0
x3 + 27 + (-27 + 3x + (-9 * x + x * x)) = 0
x3 + 27 + (-27 + 3x + (-9x + x2)) = 0

Combine like terms: 3x + -9x = -6x
x3 + 27 + (-27 + -6x + x2) = 0

Reorder the terms:
27 + -27 + -6x + x2 + x3 = 0

Combine like terms: 27 + -27 = 0
0 + -6x + x2 + x3 = 0
-6x + x2 + x3 = 0

Solving
-6x + x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-6 + x + x2) = 0

Factor a trinomial.
x((-3 + -1x)(2 + -1x)) = 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 '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {0, -3, 2}

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