108=(6)(8+x)(x)

Solution for 108=(6)(8+x)(x) equation:

Simplifying
108 = (6)(8 + x)(x)

Reorder the terms for easier multiplication:
108 = 6x(8 + x)
108 = (8 * 6x + x * 6x)
108 = (48x + 6x2)

Solving
108 = 48x + 6x2

Solving for variable 'x'.

Reorder the terms:
108 + -48x + -6x2 = 48x + -48x + 6x2 + -6x2

Combine like terms: 48x + -48x = 0
108 + -48x + -6x2 = 0 + 6x2 + -6x2
108 + -48x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
108 + -48x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(18 + -8x + -1x2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(18 + -8x + -1x2)' equal to zero and attempt to solve:

Simplifying
18 + -8x + -1x2 = 0

Solving
18 + -8x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-18 + 8x + x2 = 0

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + 8x + 18 + x2 = 0 + 18

Reorder the terms:
-18 + 18 + 8x + x2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + 8x + x2 = 0 + 18
8x + x2 = 0 + 18

Combine like terms: 0 + 18 = 18
8x + x2 = 18

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 18 + 16

Reorder the terms:
16 + 8x + x2 = 18 + 16

Combine like terms: 18 + 16 = 34
16 + 8x + x2 = 34

Factor a perfect square on the left side:
(x + 4)(x + 4) = 34

Calculate the square root of the right side: 5.830951895

Break this problem into two subproblems by setting 
(x + 4) equal to 5.830951895 and -5.830951895.

Subproblem 1
x + 4 = 5.830951895

Simplifying
x + 4 = 5.830951895

Reorder the terms:
4 + x = 5.830951895

Solving
4 + x = 5.830951895

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 5.830951895 + -4

Combine like terms: 4 + -4 = 0
0 + x = 5.830951895 + -4
x = 5.830951895 + -4

Combine like terms: 5.830951895 + -4 = 1.830951895
x = 1.830951895

Simplifying
x = 1.830951895

Subproblem 2
x + 4 = -5.830951895

Simplifying
x + 4 = -5.830951895

Reorder the terms:
4 + x = -5.830951895

Solving
4 + x = -5.830951895

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -5.830951895 + -4

Combine like terms: 4 + -4 = 0
0 + x = -5.830951895 + -4
x = -5.830951895 + -4

Combine like terms: -5.830951895 + -4 = -9.830951895
x = -9.830951895

Simplifying
x = -9.830951895

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.830951895, -9.830951895}
Solution
x = {1.830951895, -9.830951895}