(3x-9)(4x+12)=0

Solution for (3x-9)(4x+12)=0 equation:

Simplifying
(3x + -9)(4x + 12) = 0

Reorder the terms:
(-9 + 3x)(4x + 12) = 0

Reorder the terms:
(-9 + 3x)(12 + 4x) = 0

Multiply (-9 + 3x) * (12 + 4x)
(-9(12 + 4x) + 3x * (12 + 4x)) = 0
((12 * -9 + 4x * -9) + 3x * (12 + 4x)) = 0
((-108 + -36x) + 3x * (12 + 4x)) = 0
(-108 + -36x + (12 * 3x + 4x * 3x)) = 0
(-108 + -36x + (36x + 12x2)) = 0

Combine like terms: -36x + 36x = 0
(-108 + 0 + 12x2) = 0
(-108 + 12x2) = 0

Solving
-108 + 12x2 = 0

Solving for variable 'x'.

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

Add '108' to each side of the equation.
-108 + 108 + 12x2 = 0 + 108

Combine like terms: -108 + 108 = 0
0 + 12x2 = 0 + 108
12x2 = 0 + 108

Combine like terms: 0 + 108 = 108
12x2 = 108

Divide each side by '12'.
x2 = 9

Simplifying
x2 = 9

Take the square root of each side:
x = {-3, 3}