-6s(2s+5)=15

Solution for -6s(2s+5)=15 equation:

Simplifying
-6s(2s + 5) = 15

Reorder the terms:
-6s(5 + 2s) = 15
(5 * -6s + 2s * -6s) = 15
(-30s + -12s2) = 15

Solving
-30s + -12s2 = 15

Solving for variable 's'.

Reorder the terms:
-15 + -30s + -12s2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + -30s + -12s2 = 0

Factor out the Greatest Common Factor (GCF), '-3'.
-3(5 + 10s + 4s2) = 0

Ignore the factor -3.
Subproblem 1
Set the factor '(5 + 10s + 4s2)' equal to zero and attempt to solve:

Simplifying
5 + 10s + 4s2 = 0

Solving
5 + 10s + 4s2 = 0

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

Divide each side by '4'.
1.25 + 2.5s + s2 = 0

Move the constant term to the right:

Add '-1.25' to each side of the equation.
1.25 + 2.5s + -1.25 + s2 = 0 + -1.25

Reorder the terms:
1.25 + -1.25 + 2.5s + s2 = 0 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + 2.5s + s2 = 0 + -1.25
2.5s + s2 = 0 + -1.25

Combine like terms: 0 + -1.25 = -1.25
2.5s + s2 = -1.25

The s term is 2.5s.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5s + 1.5625 + s2 = -1.25 + 1.5625

Reorder the terms:
1.5625 + 2.5s + s2 = -1.25 + 1.5625

Combine like terms: -1.25 + 1.5625 = 0.3125
1.5625 + 2.5s + s2 = 0.3125

Factor a perfect square on the left side:
(s + 1.25)(s + 1.25) = 0.3125

Calculate the square root of the right side: 0.559016994

Break this problem into two subproblems by setting 
(s + 1.25) equal to 0.559016994 and -0.559016994.

Subproblem 1
s + 1.25 = 0.559016994

Simplifying
s + 1.25 = 0.559016994

Reorder the terms:
1.25 + s = 0.559016994

Solving
1.25 + s = 0.559016994

Solving for variable 's'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + s = 0.559016994 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + s = 0.559016994 + -1.25
s = 0.559016994 + -1.25

Combine like terms: 0.559016994 + -1.25 = -0.690983006
s = -0.690983006

Simplifying
s = -0.690983006

Subproblem 2
s + 1.25 = -0.559016994

Simplifying
s + 1.25 = -0.559016994

Reorder the terms:
1.25 + s = -0.559016994

Solving
1.25 + s = -0.559016994

Solving for variable 's'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + s = -0.559016994 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + s = -0.559016994 + -1.25
s = -0.559016994 + -1.25

Combine like terms: -0.559016994 + -1.25 = -1.809016994
s = -1.809016994

Simplifying
s = -1.809016994

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {-0.690983006, -1.809016994}
Solution
s = {-0.690983006, -1.809016994}