2(4s-16)5s=-5

Solution for 2(4s-16)5s=-5 equation:

Simplifying
2(4s + -16) * 5s = -5

Reorder the terms:
2(-16 + 4s) * 5s = -5

Reorder the terms for easier multiplication:
2 * 5s(-16 + 4s) = -5

Multiply 2 * 5
10s(-16 + 4s) = -5
(-16 * 10s + 4s * 10s) = -5
(-160s + 40s2) = -5

Solving
-160s + 40s2 = -5

Solving for variable 's'.

Reorder the terms:
5 + -160s + 40s2 = -5 + 5

Combine like terms: -5 + 5 = 0
5 + -160s + 40s2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(1 + -32s + 8s2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(1 + -32s + 8s2)' equal to zero and attempt to solve:

Simplifying
1 + -32s + 8s2 = 0

Solving
1 + -32s + 8s2 = 0

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

Divide each side by '8'.
0.125 + -4s + s2 = 0

Move the constant term to the right:

Add '-0.125' to each side of the equation.
0.125 + -4s + -0.125 + s2 = 0 + -0.125

Reorder the terms:
0.125 + -0.125 + -4s + s2 = 0 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + -4s + s2 = 0 + -0.125
-4s + s2 = 0 + -0.125

Combine like terms: 0 + -0.125 = -0.125
-4s + s2 = -0.125

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 = -0.125 + 4

Reorder the terms:
4 + -4s + s2 = -0.125 + 4

Combine like terms: -0.125 + 4 = 3.875
4 + -4s + s2 = 3.875

Factor a perfect square on the left side:
(s + -2)(s + -2) = 3.875

Calculate the square root of the right side: 1.968501969

Break this problem into two subproblems by setting 
(s + -2) equal to 1.968501969 and -1.968501969.

Subproblem 1
s + -2 = 1.968501969

Simplifying
s + -2 = 1.968501969

Reorder the terms:
-2 + s = 1.968501969

Solving
-2 + s = 1.968501969

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 = 1.968501969 + 2

Combine like terms: -2 + 2 = 0
0 + s = 1.968501969 + 2
s = 1.968501969 + 2

Combine like terms: 1.968501969 + 2 = 3.968501969
s = 3.968501969

Simplifying
s = 3.968501969

Subproblem 2
s + -2 = -1.968501969

Simplifying
s + -2 = -1.968501969

Reorder the terms:
-2 + s = -1.968501969

Solving
-2 + s = -1.968501969

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 = -1.968501969 + 2

Combine like terms: -2 + 2 = 0
0 + s = -1.968501969 + 2
s = -1.968501969 + 2

Combine like terms: -1.968501969 + 2 = 0.031498031
s = 0.031498031

Simplifying
s = 0.031498031

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {3.968501969, 0.031498031}
Solution
s = {3.968501969, 0.031498031}