12=.5*b*(2b-8)

Solution for 12=.5*b*(2b-8) equation:

Simplifying
12 = 0.5b(2b + -8)

Reorder the terms:
12 = 0.5b(-8 + 2b)
12 = (-8 * 0.5b + 2b * 0.5b)
12 = (-4b + 1b2)

Solving
12 = -4b + 1b2

Solving for variable 'b'.

Reorder the terms:
12 + 4b + -1b2 = -4b + 4b + 1b2 + -1b2

Combine like terms: -4b + 4b = 0
12 + 4b + -1b2 = 0 + 1b2 + -1b2
12 + 4b + -1b2 = 1b2 + -1b2

Combine like terms: 1b2 + -1b2 = 0
12 + 4b + -1b2 = 0

Factor a trinomial.
(6 + -1b)(2 + b) = 0

Subproblem 1
Set the factor '(6 + -1b)' equal to zero and attempt to solve:

Simplifying
6 + -1b = 0

Solving
6 + -1b = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1b = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1b = 0 + -6
-1b = 0 + -6

Combine like terms: 0 + -6 = -6
-1b = -6

Divide each side by '-1'.
b = 6

Simplifying
b = 6
Subproblem 2
Set the factor '(2 + b)' equal to zero and attempt to solve:

Simplifying
2 + b = 0

Solving
2 + b = 0

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

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

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

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

Simplifying
b = -2
Solution
b = {6, -2}