.5b(b+2)-12=0

Solution for .5b(b+2)-12=0 equation:

Simplifying
0.5b(b + 2) + -12 = 0

Reorder the terms:
0.5b(2 + b) + -12 = 0
(2 * 0.5b + b * 0.5b) + -12 = 0
(1b + 0.5b2) + -12 = 0

Reorder the terms:
-12 + 1b + 0.5b2 = 0

Solving
-12 + 1b + 0.5b2 = 0

Solving for variable 'b'.

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

Divide each side by '0.5'.
-24 + 2b + b2 = 0

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + 2b + 24 + b2 = 0 + 24

Reorder the terms:
-24 + 24 + 2b + b2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + 2b + b2 = 0 + 24
2b + b2 = 0 + 24

Combine like terms: 0 + 24 = 24
2b + b2 = 24

The b term is 2b.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2b + 1 + b2 = 24 + 1

Reorder the terms:
1 + 2b + b2 = 24 + 1

Combine like terms: 24 + 1 = 25
1 + 2b + b2 = 25

Factor a perfect square on the left side:
(b + 1)(b + 1) = 25

Calculate the square root of the right side: 5

Break this problem into two subproblems by setting 
(b + 1) equal to 5 and -5.

Subproblem 1
b + 1 = 5

Simplifying
b + 1 = 5

Reorder the terms:
1 + b = 5

Solving
1 + b = 5

Solving for variable 'b'.

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

Add '-1' to each side of the equation.
1 + -1 + b = 5 + -1

Combine like terms: 1 + -1 = 0
0 + b = 5 + -1
b = 5 + -1

Combine like terms: 5 + -1 = 4
b = 4

Simplifying
b = 4

Subproblem 2
b + 1 = -5

Simplifying
b + 1 = -5

Reorder the terms:
1 + b = -5

Solving
1 + b = -5

Solving for variable 'b'.

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

Add '-1' to each side of the equation.
1 + -1 + b = -5 + -1

Combine like terms: 1 + -1 = 0
0 + b = -5 + -1
b = -5 + -1

Combine like terms: -5 + -1 = -6
b = -6

Simplifying
b = -6

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {4, -6}