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

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

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

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

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

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

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

Solving
-24 + -6x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-8 + -2x + x2) = 0

Factor a trinomial.
3((-2 + -1x)(4 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
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
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 = {-2, 4}