(s+2)*(2s+4)=43.2

Solution for (s+2)*(2s+4)=43.2 equation:

Simplifying
(s + 2)(2s + 4) = 43.2

Reorder the terms:
(2 + s)(2s + 4) = 43.2

Reorder the terms:
(2 + s)(4 + 2s) = 43.2

Multiply (2 + s) * (4 + 2s)
(2(4 + 2s) + s(4 + 2s)) = 43.2
((4 * 2 + 2s * 2) + s(4 + 2s)) = 43.2
((8 + 4s) + s(4 + 2s)) = 43.2
(8 + 4s + (4 * s + 2s * s)) = 43.2
(8 + 4s + (4s + 2s2)) = 43.2

Combine like terms: 4s + 4s = 8s
(8 + 8s + 2s2) = 43.2

Solving
8 + 8s + 2s2 = 43.2

Solving for variable 's'.

Reorder the terms:
8 + -43.2 + 8s + 2s2 = 43.2 + -43.2

Combine like terms: 8 + -43.2 = -35.2
-35.2 + 8s + 2s2 = 43.2 + -43.2

Combine like terms: 43.2 + -43.2 = 0.0
-35.2 + 8s + 2s2 = 0.0

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

Divide each side by '2'.
-17.6 + 4s + s2 = 0.0

Move the constant term to the right:

Add '17.6' to each side of the equation.
-17.6 + 4s + 17.6 + s2 = 0.0 + 17.6

Reorder the terms:
-17.6 + 17.6 + 4s + s2 = 0.0 + 17.6

Combine like terms: -17.6 + 17.6 = 0.0
0.0 + 4s + s2 = 0.0 + 17.6
4s + s2 = 0.0 + 17.6

Combine like terms: 0.0 + 17.6 = 17.6
4s + s2 = 17.6

The s term is 4s.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4s + 4 + s2 = 17.6 + 4

Reorder the terms:
4 + 4s + s2 = 17.6 + 4

Combine like terms: 17.6 + 4 = 21.6
4 + 4s + s2 = 21.6

Factor a perfect square on the left side:
(s + 2)(s + 2) = 21.6

Calculate the square root of the right side: 4.647580015

Break this problem into two subproblems by setting 
(s + 2) equal to 4.647580015 and -4.647580015.

Subproblem 1
s + 2 = 4.647580015

Simplifying
s + 2 = 4.647580015

Reorder the terms:
2 + s = 4.647580015

Solving
2 + s = 4.647580015

Solving for variable 's'.

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

Add '-2' to each side of the equation.
2 + -2 + s = 4.647580015 + -2

Combine like terms: 2 + -2 = 0
0 + s = 4.647580015 + -2
s = 4.647580015 + -2

Combine like terms: 4.647580015 + -2 = 2.647580015
s = 2.647580015

Simplifying
s = 2.647580015

Subproblem 2
s + 2 = -4.647580015

Simplifying
s + 2 = -4.647580015

Reorder the terms:
2 + s = -4.647580015

Solving
2 + s = -4.647580015

Solving for variable 's'.

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

Add '-2' to each side of the equation.
2 + -2 + s = -4.647580015 + -2

Combine like terms: 2 + -2 = 0
0 + s = -4.647580015 + -2
s = -4.647580015 + -2

Combine like terms: -4.647580015 + -2 = -6.647580015
s = -6.647580015

Simplifying
s = -6.647580015

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {2.647580015, -6.647580015}