660=(2s+10)(s+4)

Solution for 660=(2s+10)(s+4) equation:

Simplifying
660 = (2s + 10)(s + 4)

Reorder the terms:
660 = (10 + 2s)(s + 4)

Reorder the terms:
660 = (10 + 2s)(4 + s)

Multiply (10 + 2s) * (4 + s)
660 = (10(4 + s) + 2s * (4 + s))
660 = ((4 * 10 + s * 10) + 2s * (4 + s))
660 = ((40 + 10s) + 2s * (4 + s))
660 = (40 + 10s + (4 * 2s + s * 2s))
660 = (40 + 10s + (8s + 2s2))

Combine like terms: 10s + 8s = 18s
660 = (40 + 18s + 2s2)

Solving
660 = 40 + 18s + 2s2

Solving for variable 's'.

Combine like terms: 660 + -40 = 620
620 + -18s + -2s2 = 40 + 18s + 2s2 + -40 + -18s + -2s2

Reorder the terms:
620 + -18s + -2s2 = 40 + -40 + 18s + -18s + 2s2 + -2s2

Combine like terms: 40 + -40 = 0
620 + -18s + -2s2 = 0 + 18s + -18s + 2s2 + -2s2
620 + -18s + -2s2 = 18s + -18s + 2s2 + -2s2

Combine like terms: 18s + -18s = 0
620 + -18s + -2s2 = 0 + 2s2 + -2s2
620 + -18s + -2s2 = 2s2 + -2s2

Combine like terms: 2s2 + -2s2 = 0
620 + -18s + -2s2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(310 + -9s + -1s2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(310 + -9s + -1s2)' equal to zero and attempt to solve:

Simplifying
310 + -9s + -1s2 = 0

Solving
310 + -9s + -1s2 = 0

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

Divide each side by '-1'.
-310 + 9s + s2 = 0

Move the constant term to the right:

Add '310' to each side of the equation.
-310 + 9s + 310 + s2 = 0 + 310

Reorder the terms:
-310 + 310 + 9s + s2 = 0 + 310

Combine like terms: -310 + 310 = 0
0 + 9s + s2 = 0 + 310
9s + s2 = 0 + 310

Combine like terms: 0 + 310 = 310
9s + s2 = 310

The s term is 9s.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9s + 20.25 + s2 = 310 + 20.25

Reorder the terms:
20.25 + 9s + s2 = 310 + 20.25

Combine like terms: 310 + 20.25 = 330.25
20.25 + 9s + s2 = 330.25

Factor a perfect square on the left side:
(s + 4.5)(s + 4.5) = 330.25

Calculate the square root of the right side: 18.172781845

Break this problem into two subproblems by setting 
(s + 4.5) equal to 18.172781845 and -18.172781845.

Subproblem 1
s + 4.5 = 18.172781845

Simplifying
s + 4.5 = 18.172781845

Reorder the terms:
4.5 + s = 18.172781845

Solving
4.5 + s = 18.172781845

Solving for variable 's'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + s = 18.172781845 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + s = 18.172781845 + -4.5
s = 18.172781845 + -4.5

Combine like terms: 18.172781845 + -4.5 = 13.672781845
s = 13.672781845

Simplifying
s = 13.672781845

Subproblem 2
s + 4.5 = -18.172781845

Simplifying
s + 4.5 = -18.172781845

Reorder the terms:
4.5 + s = -18.172781845

Solving
4.5 + s = -18.172781845

Solving for variable 's'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + s = -18.172781845 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + s = -18.172781845 + -4.5
s = -18.172781845 + -4.5

Combine like terms: -18.172781845 + -4.5 = -22.672781845
s = -22.672781845

Simplifying
s = -22.672781845

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {13.672781845, -22.672781845}
Solution
s = {13.672781845, -22.672781845}