2(b-4)-6(b+8)=12(b+4)(8b+6)

Solution for 2(b-4)-6(b+8)=12(b+4)(8b+6) equation:

Simplifying
2(b + -4) + -6(b + 8) = 12(b + 4)(8b + 6)

Reorder the terms:
2(-4 + b) + -6(b + 8) = 12(b + 4)(8b + 6)
(-4 * 2 + b * 2) + -6(b + 8) = 12(b + 4)(8b + 6)
(-8 + 2b) + -6(b + 8) = 12(b + 4)(8b + 6)

Reorder the terms:
-8 + 2b + -6(8 + b) = 12(b + 4)(8b + 6)
-8 + 2b + (8 * -6 + b * -6) = 12(b + 4)(8b + 6)
-8 + 2b + (-48 + -6b) = 12(b + 4)(8b + 6)

Reorder the terms:
-8 + -48 + 2b + -6b = 12(b + 4)(8b + 6)

Combine like terms: -8 + -48 = -56
-56 + 2b + -6b = 12(b + 4)(8b + 6)

Combine like terms: 2b + -6b = -4b
-56 + -4b = 12(b + 4)(8b + 6)

Reorder the terms:
-56 + -4b = 12(4 + b)(8b + 6)

Reorder the terms:
-56 + -4b = 12(4 + b)(6 + 8b)

Multiply (4 + b) * (6 + 8b)
-56 + -4b = 12(4(6 + 8b) + b(6 + 8b))
-56 + -4b = 12((6 * 4 + 8b * 4) + b(6 + 8b))
-56 + -4b = 12((24 + 32b) + b(6 + 8b))
-56 + -4b = 12(24 + 32b + (6 * b + 8b * b))
-56 + -4b = 12(24 + 32b + (6b + 8b2))

Combine like terms: 32b + 6b = 38b
-56 + -4b = 12(24 + 38b + 8b2)
-56 + -4b = (24 * 12 + 38b * 12 + 8b2 * 12)
-56 + -4b = (288 + 456b + 96b2)

Solving
-56 + -4b = 288 + 456b + 96b2

Solving for variable 'b'.

Reorder the terms:
-56 + -288 + -4b + -456b + -96b2 = 288 + 456b + 96b2 + -288 + -456b + -96b2

Combine like terms: -56 + -288 = -344
-344 + -4b + -456b + -96b2 = 288 + 456b + 96b2 + -288 + -456b + -96b2

Combine like terms: -4b + -456b = -460b
-344 + -460b + -96b2 = 288 + 456b + 96b2 + -288 + -456b + -96b2

Reorder the terms:
-344 + -460b + -96b2 = 288 + -288 + 456b + -456b + 96b2 + -96b2

Combine like terms: 288 + -288 = 0
-344 + -460b + -96b2 = 0 + 456b + -456b + 96b2 + -96b2
-344 + -460b + -96b2 = 456b + -456b + 96b2 + -96b2

Combine like terms: 456b + -456b = 0
-344 + -460b + -96b2 = 0 + 96b2 + -96b2
-344 + -460b + -96b2 = 96b2 + -96b2

Combine like terms: 96b2 + -96b2 = 0
-344 + -460b + -96b2 = 0

Factor out the Greatest Common Factor (GCF), '-4'.
-4(86 + 115b + 24b2) = 0

Ignore the factor -4.
Subproblem 1
Set the factor '(86 + 115b + 24b2)' equal to zero and attempt to solve:

Simplifying
86 + 115b + 24b2 = 0

Solving
86 + 115b + 24b2 = 0

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

Divide each side by '24'.
3.583333333 + 4.791666667b + b2 = 0

Move the constant term to the right:

Add '-3.583333333' to each side of the equation.
3.583333333 + 4.791666667b + -3.583333333 + b2 = 0 + -3.583333333

Reorder the terms:
3.583333333 + -3.583333333 + 4.791666667b + b2 = 0 + -3.583333333

Combine like terms: 3.583333333 + -3.583333333 = 0.000000000
0.000000000 + 4.791666667b + b2 = 0 + -3.583333333
4.791666667b + b2 = 0 + -3.583333333

Combine like terms: 0 + -3.583333333 = -3.583333333
4.791666667b + b2 = -3.583333333

The b term is 4.791666667b.  Take half its coefficient (2.395833334).
Square it (5.740017364) and add it to both sides.

Add '5.740017364' to each side of the equation.
4.791666667b + 5.740017364 + b2 = -3.583333333 + 5.740017364

Reorder the terms:
5.740017364 + 4.791666667b + b2 = -3.583333333 + 5.740017364

Combine like terms: -3.583333333 + 5.740017364 = 2.156684031
5.740017364 + 4.791666667b + b2 = 2.156684031

Factor a perfect square on the left side:
(b + 2.395833334)(b + 2.395833334) = 2.156684031

Calculate the square root of the right side: 1.468565297

Break this problem into two subproblems by setting 
(b + 2.395833334) equal to 1.468565297 and -1.468565297.

Subproblem 1
b + 2.395833334 = 1.468565297

Simplifying
b + 2.395833334 = 1.468565297

Reorder the terms:
2.395833334 + b = 1.468565297

Solving
2.395833334 + b = 1.468565297

Solving for variable 'b'.

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

Add '-2.395833334' to each side of the equation.
2.395833334 + -2.395833334 + b = 1.468565297 + -2.395833334

Combine like terms: 2.395833334 + -2.395833334 = 0.000000000
0.000000000 + b = 1.468565297 + -2.395833334
b = 1.468565297 + -2.395833334

Combine like terms: 1.468565297 + -2.395833334 = -0.927268037
b = -0.927268037

Simplifying
b = -0.927268037

Subproblem 2
b + 2.395833334 = -1.468565297

Simplifying
b + 2.395833334 = -1.468565297

Reorder the terms:
2.395833334 + b = -1.468565297

Solving
2.395833334 + b = -1.468565297

Solving for variable 'b'.

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

Add '-2.395833334' to each side of the equation.
2.395833334 + -2.395833334 + b = -1.468565297 + -2.395833334

Combine like terms: 2.395833334 + -2.395833334 = 0.000000000
0.000000000 + b = -1.468565297 + -2.395833334
b = -1.468565297 + -2.395833334

Combine like terms: -1.468565297 + -2.395833334 = -3.864398631
b = -3.864398631

Simplifying
b = -3.864398631

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {-0.927268037, -3.864398631}
Solution
b = {-0.927268037, -3.864398631}