12s^2-128s+252=0

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Solution for 12s^2-128s+252=0 equation: 


Simplifying
12s2 + -128s + 252 = 0

Reorder the terms:
252 + -128s + 12s2 = 0

Solving
252 + -128s + 12s2 = 0

Solving for variable 's'.

Factor out the Greatest Common Factor (GCF), '4'.
4(63 + -32s + 3s2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(63 + -32s + 3s2)' equal to zero and attempt to solve:

Simplifying
63 + -32s + 3s2 = 0

Solving
63 + -32s + 3s2 = 0

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

Divide each side by '3'.
21 + -10.66666667s + s2 = 0

Move the constant term to the right:

Add '-21' to each side of the equation.
21 + -10.66666667s + -21 + s2 = 0 + -21

Reorder the terms:
21 + -21 + -10.66666667s + s2 = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -10.66666667s + s2 = 0 + -21
-10.66666667s + s2 = 0 + -21

Combine like terms: 0 + -21 = -21
-10.66666667s + s2 = -21

The s term is -10.66666667s.  Take half its coefficient (-5.333333335).
Square it (28.44444446) and add it to both sides.

Add '28.44444446' to each side of the equation.
-10.66666667s + 28.44444446 + s2 = -21 + 28.44444446

Reorder the terms:
28.44444446 + -10.66666667s + s2 = -21 + 28.44444446

Combine like terms: -21 + 28.44444446 = 7.44444446
28.44444446 + -10.66666667s + s2 = 7.44444446

Factor a perfect square on the left side:
(s + -5.333333335)(s + -5.333333335) = 7.44444446

Calculate the square root of the right side: 2.728450927

Break this problem into two subproblems by setting 
(s + -5.333333335) equal to 2.728450927 and -2.728450927.


Subproblem 1
s + -5.333333335 = 2.728450927

Simplifying
s + -5.333333335 = 2.728450927

Reorder the terms:
-5.333333335 + s = 2.728450927

Solving
-5.333333335 + s = 2.728450927

Solving for variable 's'.

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

Add '5.333333335' to each side of the equation.
-5.333333335 + 5.333333335 + s = 2.728450927 + 5.333333335

Combine like terms: -5.333333335 + 5.333333335 = 0.000000000
0.000000000 + s = 2.728450927 + 5.333333335
s = 2.728450927 + 5.333333335

Combine like terms: 2.728450927 + 5.333333335 = 8.061784262
s = 8.061784262

Simplifying
s = 8.061784262


Subproblem 2
s + -5.333333335 = -2.728450927

Simplifying
s + -5.333333335 = -2.728450927

Reorder the terms:
-5.333333335 + s = -2.728450927

Solving
-5.333333335 + s = -2.728450927

Solving for variable 's'.

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

Add '5.333333335' to each side of the equation.
-5.333333335 + 5.333333335 + s = -2.728450927 + 5.333333335

Combine like terms: -5.333333335 + 5.333333335 = 0.000000000
0.000000000 + s = -2.728450927 + 5.333333335
s = -2.728450927 + 5.333333335

Combine like terms: -2.728450927 + 5.333333335 = 2.604882408
s = 2.604882408

Simplifying
s = 2.604882408


Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {8.061784262, 2.604882408}
Solution
s = {8.061784262, 2.604882408}

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