x(x+9)(x-12)=0

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Solution for x(x+9)(x-12)=0 equation: 


Simplifying
x(x + 9)(x + -12) = 0

Reorder the terms:
x(9 + x)(x + -12) = 0

Reorder the terms:
x(9 + x)(-12 + x) = 0

Multiply (9 + x) * (-12 + x)
x(9(-12 + x) + x(-12 + x)) = 0
x((-12 * 9 + x * 9) + x(-12 + x)) = 0
x((-108 + 9x) + x(-12 + x)) = 0
x(-108 + 9x + (-12 * x + x * x)) = 0
x(-108 + 9x + (-12x + x2)) = 0

Combine like terms: 9x + -12x = -3x
x(-108 + -3x + x2) = 0
(-108 * x + -3x * x + x2 * x) = 0
(-108x + -3x2 + x3) = 0

Solving
-108x + -3x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-108 + -3x + x2) = 0

Factor a trinomial.
x((-9 + -1x)(12 + -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 '(-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

Subproblem 3
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {0, -9, 12}

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