108=(10+s)(6+s)

Solution for 108=(10+s)(6+s) equation:

Simplifying
108 = (10 + s)(6 + s)

Multiply (10 + s) * (6 + s)
108 = (10(6 + s) + s(6 + s))
108 = ((6 * 10 + s * 10) + s(6 + s))
108 = ((60 + 10s) + s(6 + s))
108 = (60 + 10s + (6 * s + s * s))
108 = (60 + 10s + (6s + s2))

Combine like terms: 10s + 6s = 16s
108 = (60 + 16s + s2)

Solving
108 = 60 + 16s + s2

Solving for variable 's'.

Combine like terms: 108 + -60 = 48
48 + -16s + -1s2 = 60 + 16s + s2 + -60 + -16s + -1s2

Reorder the terms:
48 + -16s + -1s2 = 60 + -60 + 16s + -16s + s2 + -1s2

Combine like terms: 60 + -60 = 0
48 + -16s + -1s2 = 0 + 16s + -16s + s2 + -1s2
48 + -16s + -1s2 = 16s + -16s + s2 + -1s2

Combine like terms: 16s + -16s = 0
48 + -16s + -1s2 = 0 + s2 + -1s2
48 + -16s + -1s2 = s2 + -1s2

Combine like terms: s2 + -1s2 = 0
48 + -16s + -1s2 = 0

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

Divide each side by '-1'.
-48 + 16s + s2 = 0

Move the constant term to the right:

Add '48' to each side of the equation.
-48 + 16s + 48 + s2 = 0 + 48

Reorder the terms:
-48 + 48 + 16s + s2 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + 16s + s2 = 0 + 48
16s + s2 = 0 + 48

Combine like terms: 0 + 48 = 48
16s + s2 = 48

The s term is 16s.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16s + 64 + s2 = 48 + 64

Reorder the terms:
64 + 16s + s2 = 48 + 64

Combine like terms: 48 + 64 = 112
64 + 16s + s2 = 112

Factor a perfect square on the left side:
(s + 8)(s + 8) = 112

Calculate the square root of the right side: 10.583005244

Break this problem into two subproblems by setting 
(s + 8) equal to 10.583005244 and -10.583005244.

Subproblem 1
s + 8 = 10.583005244

Simplifying
s + 8 = 10.583005244

Reorder the terms:
8 + s = 10.583005244

Solving
8 + s = 10.583005244

Solving for variable 's'.

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

Add '-8' to each side of the equation.
8 + -8 + s = 10.583005244 + -8

Combine like terms: 8 + -8 = 0
0 + s = 10.583005244 + -8
s = 10.583005244 + -8

Combine like terms: 10.583005244 + -8 = 2.583005244
s = 2.583005244

Simplifying
s = 2.583005244

Subproblem 2
s + 8 = -10.583005244

Simplifying
s + 8 = -10.583005244

Reorder the terms:
8 + s = -10.583005244

Solving
8 + s = -10.583005244

Solving for variable 's'.

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

Add '-8' to each side of the equation.
8 + -8 + s = -10.583005244 + -8

Combine like terms: 8 + -8 = 0
0 + s = -10.583005244 + -8
s = -10.583005244 + -8

Combine like terms: -10.583005244 + -8 = -18.583005244
s = -18.583005244

Simplifying
s = -18.583005244

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {2.583005244, -18.583005244}