6b(b-2)=12

Solution for 6b(b-2)=12 equation:

Simplifying
6b(b + -2) = 12

Reorder the terms:
6b(-2 + b) = 12
(-2 * 6b + b * 6b) = 12
(-12b + 6b2) = 12

Solving
-12b + 6b2 = 12

Solving for variable 'b'.

Reorder the terms:
-12 + -12b + 6b2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + -12b + 6b2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-2 + -2b + b2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-2 + -2b + b2)' equal to zero and attempt to solve:

Simplifying
-2 + -2b + b2 = 0

Solving
-2 + -2b + b2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = 2 + 1

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

Combine like terms: 2 + 1 = 3
1 + -2b + b2 = 3

Factor a perfect square on the left side:
(b + -1)(b + -1) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(b + -1) equal to 1.732050808 and -1.732050808.

Subproblem 1
b + -1 = 1.732050808

Simplifying
b + -1 = 1.732050808

Reorder the terms:
-1 + b = 1.732050808

Solving
-1 + b = 1.732050808

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 = 1.732050808 + 1

Combine like terms: -1 + 1 = 0
0 + b = 1.732050808 + 1
b = 1.732050808 + 1

Combine like terms: 1.732050808 + 1 = 2.732050808
b = 2.732050808

Simplifying
b = 2.732050808

Subproblem 2
b + -1 = -1.732050808

Simplifying
b + -1 = -1.732050808

Reorder the terms:
-1 + b = -1.732050808

Solving
-1 + b = -1.732050808

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 = -1.732050808 + 1

Combine like terms: -1 + 1 = 0
0 + b = -1.732050808 + 1
b = -1.732050808 + 1

Combine like terms: -1.732050808 + 1 = -0.732050808
b = -0.732050808

Simplifying
b = -0.732050808

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {2.732050808, -0.732050808}
Solution
b = {2.732050808, -0.732050808}