-10s(s+3)=-116

Solution for -10s(s+3)=-116 equation:

Simplifying
-10s(s + 3) = -116

Reorder the terms:
-10s(3 + s) = -116
(3 * -10s + s * -10s) = -116
(-30s + -10s2) = -116

Solving
-30s + -10s2 = -116

Solving for variable 's'.

Reorder the terms:
116 + -30s + -10s2 = -116 + 116

Combine like terms: -116 + 116 = 0
116 + -30s + -10s2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(58 + -15s + -5s2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(58 + -15s + -5s2)' equal to zero and attempt to solve:

Simplifying
58 + -15s + -5s2 = 0

Solving
58 + -15s + -5s2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-11.6 + 3s + s2 = 0

Move the constant term to the right:

Add '11.6' to each side of the equation.
-11.6 + 3s + 11.6 + s2 = 0 + 11.6

Reorder the terms:
-11.6 + 11.6 + 3s + s2 = 0 + 11.6

Combine like terms: -11.6 + 11.6 = 0.0
0.0 + 3s + s2 = 0 + 11.6
3s + s2 = 0 + 11.6

Combine like terms: 0 + 11.6 = 11.6
3s + s2 = 11.6

The s term is 3s.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3s + 2.25 + s2 = 11.6 + 2.25

Reorder the terms:
2.25 + 3s + s2 = 11.6 + 2.25

Combine like terms: 11.6 + 2.25 = 13.85
2.25 + 3s + s2 = 13.85

Factor a perfect square on the left side:
(s + 1.5)(s + 1.5) = 13.85

Calculate the square root of the right side: 3.721558813

Break this problem into two subproblems by setting 
(s + 1.5) equal to 3.721558813 and -3.721558813.

Subproblem 1
s + 1.5 = 3.721558813

Simplifying
s + 1.5 = 3.721558813

Reorder the terms:
1.5 + s = 3.721558813

Solving
1.5 + s = 3.721558813

Solving for variable 's'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + s = 3.721558813 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + s = 3.721558813 + -1.5
s = 3.721558813 + -1.5

Combine like terms: 3.721558813 + -1.5 = 2.221558813
s = 2.221558813

Simplifying
s = 2.221558813

Subproblem 2
s + 1.5 = -3.721558813

Simplifying
s + 1.5 = -3.721558813

Reorder the terms:
1.5 + s = -3.721558813

Solving
1.5 + s = -3.721558813

Solving for variable 's'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + s = -3.721558813 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + s = -3.721558813 + -1.5
s = -3.721558813 + -1.5

Combine like terms: -3.721558813 + -1.5 = -5.221558813
s = -5.221558813

Simplifying
s = -5.221558813

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {2.221558813, -5.221558813}
Solution
s = {2.221558813, -5.221558813}