(x+9)(3x-12)=0

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Solution for (x+9)(3x-12)=0 equation: 


Simplifying
(x + 9)(3x + -12) = 0

Reorder the terms:
(9 + x)(3x + -12) = 0

Reorder the terms:
(9 + x)(-12 + 3x) = 0

Multiply (9 + x) * (-12 + 3x)
(9(-12 + 3x) + x(-12 + 3x)) = 0
((-12 * 9 + 3x * 9) + x(-12 + 3x)) = 0
((-108 + 27x) + x(-12 + 3x)) = 0
(-108 + 27x + (-12 * x + 3x * x)) = 0
(-108 + 27x + (-12x + 3x2)) = 0

Combine like terms: 27x + -12x = 15x
(-108 + 15x + 3x2) = 0

Solving
-108 + 15x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-36 + 5x + x2) = 0

Factor a trinomial.
3((-9 + -1x)(4 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
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 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-9, 4}

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