12(x+6)(x-8)=0

Solution for 12(x+6)(x-8)=0 equation:

Simplifying
12(x + 6)(x + -8) = 0

Reorder the terms:
12(6 + x)(x + -8) = 0

Reorder the terms:
12(6 + x)(-8 + x) = 0

Multiply (6 + x) * (-8 + x)
12(6(-8 + x) + x(-8 + x)) = 0
12((-8 * 6 + x * 6) + x(-8 + x)) = 0
12((-48 + 6x) + x(-8 + x)) = 0
12(-48 + 6x + (-8 * x + x * x)) = 0
12(-48 + 6x + (-8x + x2)) = 0

Combine like terms: 6x + -8x = -2x
12(-48 + -2x + x2) = 0
(-48 * 12 + -2x * 12 + x2 * 12) = 0
(-576 + -24x + 12x2) = 0

Solving
-576 + -24x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(-48 + -2x + x2) = 0

Factor a trinomial.
12((-6 + -1x)(8 + -1x)) = 0

Ignore the factor 12.
Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-6, 8}