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

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

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

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

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

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

Combine like terms: 4x + -6x = -2x
3(-24 + -2x + x2) = 0
(-24 * 3 + -2x * 3 + x2 * 3) = 0
(-72 + -6x + 3x2) = 0

Solving
-72 + -6x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-24 + -2x + x2) = 0

Factor a trinomial.
3((-4 + -1x)(6 + -1x)) = 0

Ignore the factor 3.
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 '(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
Solution
x = {-4, 6}