(x+6)((3(x-2)))=

Solution for (x+6)((3(x-2)))= equation:

Simplifying
(x + 6)(3(x + -2)) = 0

Reorder the terms:
(6 + x)(3(x + -2)) = 0

Reorder the terms:
(6 + x)(3(-2 + x)) = 0
(6 + x)((-2 * 3 + x * 3)) = 0
(6 + x)((-6 + 3x)) = 0

Multiply (6 + x) * (-6 + 3x)
(6(-6 + 3x) + x(-6 + 3x)) = 0
((-6 * 6 + 3x * 6) + x(-6 + 3x)) = 0
((-36 + 18x) + x(-6 + 3x)) = 0
(-36 + 18x + (-6 * x + 3x * x)) = 0
(-36 + 18x + (-6x + 3x2)) = 0

Combine like terms: 18x + -6x = 12x
(-36 + 12x + 3x2) = 0

Solving
-36 + 12x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-12 + 4x + x2) = 0

Factor a trinomial.
3((-6 + -1x)(2 + -1x)) = 0

Ignore the factor 3.
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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-6, 2}