6(3x-6)(4+x)=0

Solution for 6(3x-6)(4+x)=0 equation:

Simplifying
6(3x + -6)(4 + x) = 0

Reorder the terms:
6(-6 + 3x)(4 + x) = 0

Multiply (-6 + 3x) * (4 + x)
6(-6(4 + x) + 3x * (4 + x)) = 0
6((4 * -6 + x * -6) + 3x * (4 + x)) = 0
6((-24 + -6x) + 3x * (4 + x)) = 0
6(-24 + -6x + (4 * 3x + x * 3x)) = 0
6(-24 + -6x + (12x + 3x2)) = 0

Combine like terms: -6x + 12x = 6x
6(-24 + 6x + 3x2) = 0
(-24 * 6 + 6x * 6 + 3x2 * 6) = 0
(-144 + 36x + 18x2) = 0

Solving
-144 + 36x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '18'.
18(-8 + 2x + x2) = 0

Factor a trinomial.
18((-4 + -1x)(2 + -1x)) = 0

Ignore the factor 18.
Subproblem 1
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
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 = {-4, 2}