s(2s+4)=28

Solution for s(2s+4)=28 equation:

Simplifying
s(2s + 4) = 28

Reorder the terms:
s(4 + 2s) = 28
(4 * s + 2s * s) = 28
(4s + 2s2) = 28

Solving
4s + 2s2 = 28

Solving for variable 's'.

Reorder the terms:
-28 + 4s + 2s2 = 28 + -28

Combine like terms: 28 + -28 = 0
-28 + 4s + 2s2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-14 + 2s + s2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-14 + 2s + s2)' equal to zero and attempt to solve:

Simplifying
-14 + 2s + s2 = 0

Solving
-14 + 2s + s2 = 0

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + 2s + 14 + s2 = 0 + 14

Reorder the terms:
-14 + 14 + 2s + s2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + 2s + s2 = 0 + 14
2s + s2 = 0 + 14

Combine like terms: 0 + 14 = 14
2s + s2 = 14

The s term is 2s.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2s + 1 + s2 = 14 + 1

Reorder the terms:
1 + 2s + s2 = 14 + 1

Combine like terms: 14 + 1 = 15
1 + 2s + s2 = 15

Factor a perfect square on the left side:
(s + 1)(s + 1) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(s + 1) equal to 3.872983346 and -3.872983346.

Subproblem 1
s + 1 = 3.872983346

Simplifying
s + 1 = 3.872983346

Reorder the terms:
1 + s = 3.872983346

Solving
1 + s = 3.872983346

Solving for variable 's'.

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

Add '-1' to each side of the equation.
1 + -1 + s = 3.872983346 + -1

Combine like terms: 1 + -1 = 0
0 + s = 3.872983346 + -1
s = 3.872983346 + -1

Combine like terms: 3.872983346 + -1 = 2.872983346
s = 2.872983346

Simplifying
s = 2.872983346

Subproblem 2
s + 1 = -3.872983346

Simplifying
s + 1 = -3.872983346

Reorder the terms:
1 + s = -3.872983346

Solving
1 + s = -3.872983346

Solving for variable 's'.

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

Add '-1' to each side of the equation.
1 + -1 + s = -3.872983346 + -1

Combine like terms: 1 + -1 = 0
0 + s = -3.872983346 + -1
s = -3.872983346 + -1

Combine like terms: -3.872983346 + -1 = -4.872983346
s = -4.872983346

Simplifying
s = -4.872983346

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {2.872983346, -4.872983346}
Solution
s = {2.872983346, -4.872983346}