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

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

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

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

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

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

Multiply (-6 + x) * (3 + x)
4(-6(3 + x) + x(3 + x)) = 0
4((3 * -6 + x * -6) + x(3 + x)) = 0
4((-18 + -6x) + x(3 + x)) = 0
4(-18 + -6x + (3 * x + x * x)) = 0
4(-18 + -6x + (3x + x2)) = 0

Combine like terms: -6x + 3x = -3x
4(-18 + -3x + x2) = 0
(-18 * 4 + -3x * 4 + x2 * 4) = 0
(-72 + -12x + 4x2) = 0

Solving
-72 + -12x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-18 + -3x + x2) = 0

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

Ignore the factor 4.
Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3
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 = {-3, 6}