s*s-12s+12=0

Solution for s*s-12s+12=0 equation:

Simplifying
s * s + -12s + 12 = 0

Multiply s * s
s2 + -12s + 12 = 0

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

Solving
12 + -12s + s2 = 0

Solving for variable 's'.

Begin completing the square.

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + -12s + -12 + s2 = 0 + -12

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

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

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

The s term is -12s.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12s + 36 + s2 = -12 + 36

Reorder the terms:
36 + -12s + s2 = -12 + 36

Combine like terms: -12 + 36 = 24
36 + -12s + s2 = 24

Factor a perfect square on the left side:
(s + -6)(s + -6) = 24

Calculate the square root of the right side: 4.898979486

Break this problem into two subproblems by setting 
(s + -6) equal to 4.898979486 and -4.898979486.

Subproblem 1
s + -6 = 4.898979486

Simplifying
s + -6 = 4.898979486

Reorder the terms:
-6 + s = 4.898979486

Solving
-6 + s = 4.898979486

Solving for variable 's'.

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

Add '6' to each side of the equation.
-6 + 6 + s = 4.898979486 + 6

Combine like terms: -6 + 6 = 0
0 + s = 4.898979486 + 6
s = 4.898979486 + 6

Combine like terms: 4.898979486 + 6 = 10.898979486
s = 10.898979486

Simplifying
s = 10.898979486

Subproblem 2
s + -6 = -4.898979486

Simplifying
s + -6 = -4.898979486

Reorder the terms:
-6 + s = -4.898979486

Solving
-6 + s = -4.898979486

Solving for variable 's'.

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

Add '6' to each side of the equation.
-6 + 6 + s = -4.898979486 + 6

Combine like terms: -6 + 6 = 0
0 + s = -4.898979486 + 6
s = -4.898979486 + 6

Combine like terms: -4.898979486 + 6 = 1.101020514
s = 1.101020514

Simplifying
s = 1.101020514

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {10.898979486, 1.101020514}