3(x+6)(x+12)=75

Solution for 3(x+6)(x+12)=75 equation:

Simplifying
3(x + 6)(x + 12) = 75

Reorder the terms:
3(6 + x)(x + 12) = 75

Reorder the terms:
3(6 + x)(12 + x) = 75

Multiply (6 + x) * (12 + x)
3(6(12 + x) + x(12 + x)) = 75
3((12 * 6 + x * 6) + x(12 + x)) = 75
3((72 + 6x) + x(12 + x)) = 75
3(72 + 6x + (12 * x + x * x)) = 75
3(72 + 6x + (12x + x2)) = 75

Combine like terms: 6x + 12x = 18x
3(72 + 18x + x2) = 75
(72 * 3 + 18x * 3 + x2 * 3) = 75
(216 + 54x + 3x2) = 75

Solving
216 + 54x + 3x2 = 75

Solving for variable 'x'.

Reorder the terms:
216 + -75 + 54x + 3x2 = 75 + -75

Combine like terms: 216 + -75 = 141
141 + 54x + 3x2 = 75 + -75

Combine like terms: 75 + -75 = 0
141 + 54x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(47 + 18x + x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(47 + 18x + x2)' equal to zero and attempt to solve:

Simplifying
47 + 18x + x2 = 0

Solving
47 + 18x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-47' to each side of the equation.
47 + 18x + -47 + x2 = 0 + -47

Reorder the terms:
47 + -47 + 18x + x2 = 0 + -47

Combine like terms: 47 + -47 = 0
0 + 18x + x2 = 0 + -47
18x + x2 = 0 + -47

Combine like terms: 0 + -47 = -47
18x + x2 = -47

The x term is 18x.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18x + 81 + x2 = -47 + 81

Reorder the terms:
81 + 18x + x2 = -47 + 81

Combine like terms: -47 + 81 = 34
81 + 18x + x2 = 34

Factor a perfect square on the left side:
(x + 9)(x + 9) = 34

Calculate the square root of the right side: 5.830951895

Break this problem into two subproblems by setting 
(x + 9) equal to 5.830951895 and -5.830951895.

Subproblem 1
x + 9 = 5.830951895

Simplifying
x + 9 = 5.830951895

Reorder the terms:
9 + x = 5.830951895

Solving
9 + x = 5.830951895

Solving for variable 'x'.

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

Add '-9' to each side of the equation.
9 + -9 + x = 5.830951895 + -9

Combine like terms: 9 + -9 = 0
0 + x = 5.830951895 + -9
x = 5.830951895 + -9

Combine like terms: 5.830951895 + -9 = -3.169048105
x = -3.169048105

Simplifying
x = -3.169048105

Subproblem 2
x + 9 = -5.830951895

Simplifying
x + 9 = -5.830951895

Reorder the terms:
9 + x = -5.830951895

Solving
9 + x = -5.830951895

Solving for variable 'x'.

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

Add '-9' to each side of the equation.
9 + -9 + x = -5.830951895 + -9

Combine like terms: 9 + -9 = 0
0 + x = -5.830951895 + -9
x = -5.830951895 + -9

Combine like terms: -5.830951895 + -9 = -14.830951895
x = -14.830951895

Simplifying
x = -14.830951895

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.169048105, -14.830951895}
Solution
x = {-3.169048105, -14.830951895}