12(b+12)+6=9(b-2)9b

Solution for 12(b+12)+6=9(b-2)9b equation:

Simplifying
12(b + 12) + 6 = 9(b + -2) * 9b

Reorder the terms:
12(12 + b) + 6 = 9(b + -2) * 9b
(12 * 12 + b * 12) + 6 = 9(b + -2) * 9b
(144 + 12b) + 6 = 9(b + -2) * 9b

Reorder the terms:
144 + 6 + 12b = 9(b + -2) * 9b

Combine like terms: 144 + 6 = 150
150 + 12b = 9(b + -2) * 9b

Reorder the terms:
150 + 12b = 9(-2 + b) * 9b

Reorder the terms for easier multiplication:
150 + 12b = 9 * 9b(-2 + b)

Multiply 9 * 9
150 + 12b = 81b(-2 + b)
150 + 12b = (-2 * 81b + b * 81b)
150 + 12b = (-162b + 81b2)

Solving
150 + 12b = -162b + 81b2

Solving for variable 'b'.

Combine like terms: 12b + 162b = 174b
150 + 174b + -81b2 = -162b + 81b2 + 162b + -81b2

Reorder the terms:
150 + 174b + -81b2 = -162b + 162b + 81b2 + -81b2

Combine like terms: -162b + 162b = 0
150 + 174b + -81b2 = 0 + 81b2 + -81b2
150 + 174b + -81b2 = 81b2 + -81b2

Combine like terms: 81b2 + -81b2 = 0
150 + 174b + -81b2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(50 + 58b + -27b2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(50 + 58b + -27b2)' equal to zero and attempt to solve:

Simplifying
50 + 58b + -27b2 = 0

Solving
50 + 58b + -27b2 = 0

Begin completing the square.  Divide all terms by
-27 the coefficient of the squared term: 

Divide each side by '-27'.
-1.851851852 + -2.148148148b + b2 = 0

Move the constant term to the right:

Add '1.851851852' to each side of the equation.
-1.851851852 + -2.148148148b + 1.851851852 + b2 = 0 + 1.851851852

Reorder the terms:
-1.851851852 + 1.851851852 + -2.148148148b + b2 = 0 + 1.851851852

Combine like terms: -1.851851852 + 1.851851852 = 0.000000000
0.000000000 + -2.148148148b + b2 = 0 + 1.851851852
-2.148148148b + b2 = 0 + 1.851851852

Combine like terms: 0 + 1.851851852 = 1.851851852
-2.148148148b + b2 = 1.851851852

The b term is -2.148148148b.  Take half its coefficient (-1.074074074).
Square it (1.153635116) and add it to both sides.

Add '1.153635116' to each side of the equation.
-2.148148148b + 1.153635116 + b2 = 1.851851852 + 1.153635116

Reorder the terms:
1.153635116 + -2.148148148b + b2 = 1.851851852 + 1.153635116

Combine like terms: 1.851851852 + 1.153635116 = 3.005486968
1.153635116 + -2.148148148b + b2 = 3.005486968

Factor a perfect square on the left side:
(b + -1.074074074)(b + -1.074074074) = 3.005486968

Calculate the square root of the right side: 1.733634035

Break this problem into two subproblems by setting 
(b + -1.074074074) equal to 1.733634035 and -1.733634035.

Subproblem 1
b + -1.074074074 = 1.733634035

Simplifying
b + -1.074074074 = 1.733634035

Reorder the terms:
-1.074074074 + b = 1.733634035

Solving
-1.074074074 + b = 1.733634035

Solving for variable 'b'.

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

Add '1.074074074' to each side of the equation.
-1.074074074 + 1.074074074 + b = 1.733634035 + 1.074074074

Combine like terms: -1.074074074 + 1.074074074 = 0.000000000
0.000000000 + b = 1.733634035 + 1.074074074
b = 1.733634035 + 1.074074074

Combine like terms: 1.733634035 + 1.074074074 = 2.807708109
b = 2.807708109

Simplifying
b = 2.807708109

Subproblem 2
b + -1.074074074 = -1.733634035

Simplifying
b + -1.074074074 = -1.733634035

Reorder the terms:
-1.074074074 + b = -1.733634035

Solving
-1.074074074 + b = -1.733634035

Solving for variable 'b'.

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

Add '1.074074074' to each side of the equation.
-1.074074074 + 1.074074074 + b = -1.733634035 + 1.074074074

Combine like terms: -1.074074074 + 1.074074074 = 0.000000000
0.000000000 + b = -1.733634035 + 1.074074074
b = -1.733634035 + 1.074074074

Combine like terms: -1.733634035 + 1.074074074 = -0.659559961
b = -0.659559961

Simplifying
b = -0.659559961

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {2.807708109, -0.659559961}
Solution
b = {2.807708109, -0.659559961}