10b^2-23b-12=0

Solution for 10b^2-23b-12=0 equation:

Simplifying
10b2 + -23b + -12 = 0

Reorder the terms:
-12 + -23b + 10b2 = 0

Solving
-12 + -23b + 10b2 = 0

Solving for variable 'b'.

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

Divide each side by '10'.
-1.2 + -2.3b + b2 = 0

Move the constant term to the right:

Add '1.2' to each side of the equation.
-1.2 + -2.3b + 1.2 + b2 = 0 + 1.2

Reorder the terms:
-1.2 + 1.2 + -2.3b + b2 = 0 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + -2.3b + b2 = 0 + 1.2
-2.3b + b2 = 0 + 1.2

Combine like terms: 0 + 1.2 = 1.2
-2.3b + b2 = 1.2

The b term is -2.3b.  Take half its coefficient (-1.15).
Square it (1.3225) and add it to both sides.

Add '1.3225' to each side of the equation.
-2.3b + 1.3225 + b2 = 1.2 + 1.3225

Reorder the terms:
1.3225 + -2.3b + b2 = 1.2 + 1.3225

Combine like terms: 1.2 + 1.3225 = 2.5225
1.3225 + -2.3b + b2 = 2.5225

Factor a perfect square on the left side:
(b + -1.15)(b + -1.15) = 2.5225

Calculate the square root of the right side: 1.588238017

Break this problem into two subproblems by setting 
(b + -1.15) equal to 1.588238017 and -1.588238017.

Subproblem 1
b + -1.15 = 1.588238017

Simplifying
b + -1.15 = 1.588238017

Reorder the terms:
-1.15 + b = 1.588238017

Solving
-1.15 + b = 1.588238017

Solving for variable 'b'.

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

Add '1.15' to each side of the equation.
-1.15 + 1.15 + b = 1.588238017 + 1.15

Combine like terms: -1.15 + 1.15 = 0.00
0.00 + b = 1.588238017 + 1.15
b = 1.588238017 + 1.15

Combine like terms: 1.588238017 + 1.15 = 2.738238017
b = 2.738238017

Simplifying
b = 2.738238017

Subproblem 2
b + -1.15 = -1.588238017

Simplifying
b + -1.15 = -1.588238017

Reorder the terms:
-1.15 + b = -1.588238017

Solving
-1.15 + b = -1.588238017

Solving for variable 'b'.

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

Add '1.15' to each side of the equation.
-1.15 + 1.15 + b = -1.588238017 + 1.15

Combine like terms: -1.15 + 1.15 = 0.00
0.00 + b = -1.588238017 + 1.15
b = -1.588238017 + 1.15

Combine like terms: -1.588238017 + 1.15 = -0.438238017
b = -0.438238017

Simplifying
b = -0.438238017

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {2.738238017, -0.438238017}