-2(-3s-8)s=7

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Solution for -2(-3s-8)s=7 equation: 


Simplifying
-2(-3s + -8) * s = 7

Reorder the terms:
-2(-8 + -3s) * s = 7

Reorder the terms for easier multiplication:
-2s(-8 + -3s) = 7
(-8 * -2s + -3s * -2s) = 7
(16s + 6s2) = 7

Solving
16s + 6s2 = 7

Solving for variable 's'.

Reorder the terms:
-7 + 16s + 6s2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + 16s + 6s2 = 0

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

Divide each side by '6'.
-1.166666667 + 2.666666667s + s2 = 0

Move the constant term to the right:

Add '1.166666667' to each side of the equation.
-1.166666667 + 2.666666667s + 1.166666667 + s2 = 0 + 1.166666667

Reorder the terms:
-1.166666667 + 1.166666667 + 2.666666667s + s2 = 0 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + 2.666666667s + s2 = 0 + 1.166666667
2.666666667s + s2 = 0 + 1.166666667

Combine like terms: 0 + 1.166666667 = 1.166666667
2.666666667s + s2 = 1.166666667

The s term is 2.666666667s.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667s + 1.777777780 + s2 = 1.166666667 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667s + s2 = 1.166666667 + 1.777777780

Combine like terms: 1.166666667 + 1.777777780 = 2.944444447
1.777777780 + 2.666666667s + s2 = 2.944444447

Factor a perfect square on the left side:
(s + 1.333333334)(s + 1.333333334) = 2.944444447

Calculate the square root of the right side: 1.715938358

Break this problem into two subproblems by setting 
(s + 1.333333334) equal to 1.715938358 and -1.715938358.


Subproblem 1
s + 1.333333334 = 1.715938358

Simplifying
s + 1.333333334 = 1.715938358

Reorder the terms:
1.333333334 + s = 1.715938358

Solving
1.333333334 + s = 1.715938358

Solving for variable 's'.

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

Add '-1.333333334' to each side of the equation.
1.333333334 + -1.333333334 + s = 1.715938358 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + s = 1.715938358 + -1.333333334
s = 1.715938358 + -1.333333334

Combine like terms: 1.715938358 + -1.333333334 = 0.382605024
s = 0.382605024

Simplifying
s = 0.382605024


Subproblem 2
s + 1.333333334 = -1.715938358

Simplifying
s + 1.333333334 = -1.715938358

Reorder the terms:
1.333333334 + s = -1.715938358

Solving
1.333333334 + s = -1.715938358

Solving for variable 's'.

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

Add '-1.333333334' to each side of the equation.
1.333333334 + -1.333333334 + s = -1.715938358 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + s = -1.715938358 + -1.333333334
s = -1.715938358 + -1.333333334

Combine like terms: -1.715938358 + -1.333333334 = -3.049271692
s = -3.049271692

Simplifying
s = -3.049271692


Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {0.382605024, -3.049271692}

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