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

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

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

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

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

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

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

Solving
40 + 18s + 2s2 = 660

Solving for variable 's'.

Reorder the terms:
40 + -660 + 18s + 2s2 = 660 + -660

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

Combine like terms: 660 + -660 = 0
-620 + 18s + 2s2 = 0

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

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

Simplifying
-310 + 9s + s2 = 0

Solving
-310 + 9s + s2 = 0

Begin completing the square.

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}