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

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

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

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

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

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

Combine like terms: 12x + -6x = 6x
4(-24 + 6x + 3x2) = 0
(-24 * 4 + 6x * 4 + 3x2 * 4) = 0
(-96 + 24x + 12x2) = 0

Solving
-96 + 24x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(-8 + 2x + x2) = 0

Factor a trinomial.
12((-4 + -1x)(2 + -1x)) = 0

Ignore the factor 12.
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}