log(12+2b)=log(b^2-4b)

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Solution for log(12+2b)=log(b^2-4b) equation: 


Simplifying
log(12 + 2b) = log(b2 + -4b)
(12 * glo + 2b * glo) = log(b2 + -4b)

Reorder the terms:
(2bglo + 12glo) = log(b2 + -4b)
(2bglo + 12glo) = log(b2 + -4b)

Reorder the terms:
2bglo + 12glo = glo(-4b + b2)
2bglo + 12glo = (-4b * glo + b2 * glo)
2bglo + 12glo = (-4bglo + b2glo)

Solving
2bglo + 12glo = -4bglo + b2glo

Solving for variable 'b'.

Reorder the terms:
2bglo + 4bglo + -1b2glo + 12glo = -4bglo + b2glo + 4bglo + -1b2glo

Combine like terms: 2bglo + 4bglo = 6bglo
6bglo + -1b2glo + 12glo = -4bglo + b2glo + 4bglo + -1b2glo

Reorder the terms:
6bglo + -1b2glo + 12glo = -4bglo + 4bglo + b2glo + -1b2glo

Combine like terms: -4bglo + 4bglo = 0
6bglo + -1b2glo + 12glo = 0 + b2glo + -1b2glo
6bglo + -1b2glo + 12glo = b2glo + -1b2glo

Combine like terms: b2glo + -1b2glo = 0
6bglo + -1b2glo + 12glo = 0

Factor out the Greatest Common Factor (GCF), 'glo'.
glo(6b + -1b2 + 12) = 0


Subproblem 1
Set the factor 'glo' equal to zero and attempt to solve:

Simplifying
glo = 0

Solving
glo = 0

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

Add '-1glo' to each side of the equation.
glo + -1glo = 0 + -1glo
Remove the zero:
0 = -1glo

Simplifying
0 = -1glo

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(6b + -1b2 + 12)' equal to zero and attempt to solve:

Simplifying
6b + -1b2 + 12 = 0

Reorder the terms:
12 + 6b + -1b2 = 0

Solving
12 + 6b + -1b2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-12 + -6b + b2 = 0

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -6b + 12 + b2 = 0 + 12

Reorder the terms:
-12 + 12 + -6b + b2 = 0 + 12

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

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

The b term is -6b.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6b + 9 + b2 = 12 + 9

Reorder the terms:
9 + -6b + b2 = 12 + 9

Combine like terms: 12 + 9 = 21
9 + -6b + b2 = 21

Factor a perfect square on the left side:
(b + -3)(b + -3) = 21

Calculate the square root of the right side: 4.582575695

Break this problem into two subproblems by setting 
(b + -3) equal to 4.582575695 and -4.582575695.


Subproblem 1
b + -3 = 4.582575695

Simplifying
b + -3 = 4.582575695

Reorder the terms:
-3 + b = 4.582575695

Solving
-3 + b = 4.582575695

Solving for variable 'b'.

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

Add '3' to each side of the equation.
-3 + 3 + b = 4.582575695 + 3

Combine like terms: -3 + 3 = 0
0 + b = 4.582575695 + 3
b = 4.582575695 + 3

Combine like terms: 4.582575695 + 3 = 7.582575695
b = 7.582575695

Simplifying
b = 7.582575695


Subproblem 2
b + -3 = -4.582575695

Simplifying
b + -3 = -4.582575695

Reorder the terms:
-3 + b = -4.582575695

Solving
-3 + b = -4.582575695

Solving for variable 'b'.

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

Add '3' to each side of the equation.
-3 + 3 + b = -4.582575695 + 3

Combine like terms: -3 + 3 = 0
0 + b = -4.582575695 + 3
b = -4.582575695 + 3

Combine like terms: -4.582575695 + 3 = -1.582575695
b = -1.582575695

Simplifying
b = -1.582575695


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {7.582575695, -1.582575695}
Solution
b = {7.582575695, -1.582575695}

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