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

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


Simplifying
(x + 3)(x + -9) * x = 0

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

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

Reorder the terms for easier multiplication:
x(3 + x)(-9 + x) = 0

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

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

Solving
-27x + -6x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-27 + -6x + x2) = 0

Factor a trinomial.
x((-3 + -1x)(9 + -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 '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {0, -3, 9}

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