9b^2-18b-102=-6

Solution for 9b^2-18b-102=-6 equation:

Simplifying
9b2 + -18b + -102 = -6

Reorder the terms:
-102 + -18b + 9b2 = -6

Solving
-102 + -18b + 9b2 = -6

Solving for variable 'b'.

Reorder the terms:
-102 + 6 + -18b + 9b2 = -6 + 6

Combine like terms: -102 + 6 = -96
-96 + -18b + 9b2 = -6 + 6

Combine like terms: -6 + 6 = 0
-96 + -18b + 9b2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-32 + -6b + 3b2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-32 + -6b + 3b2)' equal to zero and attempt to solve:

Simplifying
-32 + -6b + 3b2 = 0

Solving
-32 + -6b + 3b2 = 0

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

Divide each side by '3'.
-10.66666667 + -2b + b2 = 0

Move the constant term to the right:

Add '10.66666667' to each side of the equation.
-10.66666667 + -2b + 10.66666667 + b2 = 0 + 10.66666667

Reorder the terms:
-10.66666667 + 10.66666667 + -2b + b2 = 0 + 10.66666667

Combine like terms: -10.66666667 + 10.66666667 = 0.00000000
0.00000000 + -2b + b2 = 0 + 10.66666667
-2b + b2 = 0 + 10.66666667

Combine like terms: 0 + 10.66666667 = 10.66666667
-2b + b2 = 10.66666667

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 = 10.66666667 + 1

Reorder the terms:
1 + -2b + b2 = 10.66666667 + 1

Combine like terms: 10.66666667 + 1 = 11.66666667
1 + -2b + b2 = 11.66666667

Factor a perfect square on the left side:
(b + -1)(b + -1) = 11.66666667

Calculate the square root of the right side: 3.415650256

Break this problem into two subproblems by setting 
(b + -1) equal to 3.415650256 and -3.415650256.

Subproblem 1
b + -1 = 3.415650256

Simplifying
b + -1 = 3.415650256

Reorder the terms:
-1 + b = 3.415650256

Solving
-1 + b = 3.415650256

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 = 3.415650256 + 1

Combine like terms: -1 + 1 = 0
0 + b = 3.415650256 + 1
b = 3.415650256 + 1

Combine like terms: 3.415650256 + 1 = 4.415650256
b = 4.415650256

Simplifying
b = 4.415650256

Subproblem 2
b + -1 = -3.415650256

Simplifying
b + -1 = -3.415650256

Reorder the terms:
-1 + b = -3.415650256

Solving
-1 + b = -3.415650256

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 = -3.415650256 + 1

Combine like terms: -1 + 1 = 0
0 + b = -3.415650256 + 1
b = -3.415650256 + 1

Combine like terms: -3.415650256 + 1 = -2.415650256
b = -2.415650256

Simplifying
b = -2.415650256

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {4.415650256, -2.415650256}
Solution
b = {4.415650256, -2.415650256}