-6(2s+8)2s=38

Solution for -6(2s+8)2s=38 equation:

Simplifying
-6(2s + 8) * 2s = 38

Reorder the terms:
-6(8 + 2s) * 2s = 38

Reorder the terms for easier multiplication:
-6 * 2s(8 + 2s) = 38

Multiply -6 * 2
-12s(8 + 2s) = 38
(8 * -12s + 2s * -12s) = 38
(-96s + -24s2) = 38

Solving
-96s + -24s2 = 38

Solving for variable 's'.

Reorder the terms:
-38 + -96s + -24s2 = 38 + -38

Combine like terms: 38 + -38 = 0
-38 + -96s + -24s2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(19 + 48s + 12s2) = 0

Ignore the factor -2.
Subproblem 1
Set the factor '(19 + 48s + 12s2)' equal to zero and attempt to solve:

Simplifying
19 + 48s + 12s2 = 0

Solving
19 + 48s + 12s2 = 0

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

Divide each side by '12'.
1.583333333 + 4s + s2 = 0

Move the constant term to the right:

Add '-1.583333333' to each side of the equation.
1.583333333 + 4s + -1.583333333 + s2 = 0 + -1.583333333

Reorder the terms:
1.583333333 + -1.583333333 + 4s + s2 = 0 + -1.583333333

Combine like terms: 1.583333333 + -1.583333333 = 0.000000000
0.000000000 + 4s + s2 = 0 + -1.583333333
4s + s2 = 0 + -1.583333333

Combine like terms: 0 + -1.583333333 = -1.583333333
4s + s2 = -1.583333333

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 = -1.583333333 + 4

Reorder the terms:
4 + 4s + s2 = -1.583333333 + 4

Combine like terms: -1.583333333 + 4 = 2.416666667
4 + 4s + s2 = 2.416666667

Factor a perfect square on the left side:
(s + 2)(s + 2) = 2.416666667

Calculate the square root of the right side: 1.554563176

Break this problem into two subproblems by setting 
(s + 2) equal to 1.554563176 and -1.554563176.

Subproblem 1
s + 2 = 1.554563176

Simplifying
s + 2 = 1.554563176

Reorder the terms:
2 + s = 1.554563176

Solving
2 + s = 1.554563176

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 = 1.554563176 + -2

Combine like terms: 2 + -2 = 0
0 + s = 1.554563176 + -2
s = 1.554563176 + -2

Combine like terms: 1.554563176 + -2 = -0.445436824
s = -0.445436824

Simplifying
s = -0.445436824

Subproblem 2
s + 2 = -1.554563176

Simplifying
s + 2 = -1.554563176

Reorder the terms:
2 + s = -1.554563176

Solving
2 + s = -1.554563176

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 = -1.554563176 + -2

Combine like terms: 2 + -2 = 0
0 + s = -1.554563176 + -2
s = -1.554563176 + -2

Combine like terms: -1.554563176 + -2 = -3.554563176
s = -3.554563176

Simplifying
s = -3.554563176

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {-0.445436824, -3.554563176}
Solution
s = {-0.445436824, -3.554563176}