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

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

Simplifying
4(x + 3)(6 + -1x) = 0

Reorder the terms:
4(3 + x)(6 + -1x) = 0

Multiply (3 + x) * (6 + -1x)
4(3(6 + -1x) + x(6 + -1x)) = 0
4((6 * 3 + -1x * 3) + x(6 + -1x)) = 0
4((18 + -3x) + x(6 + -1x)) = 0
4(18 + -3x + (6 * x + -1x * x)) = 0
4(18 + -3x + (6x + -1x2)) = 0

Combine like terms: -3x + 6x = 3x
4(18 + 3x + -1x2) = 0
(18 * 4 + 3x * 4 + -1x2 * 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 + -1x2) = 0

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

Ignore the factor 4.
Subproblem 1
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
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

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

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

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