3(b+3)4b+8=4(b+8)

Solution for 3(b+3)4b+8=4(b+8) equation:

Simplifying
3(b + 3) * 4b + 8 = 4(b + 8)

Reorder the terms:
3(3 + b) * 4b + 8 = 4(b + 8)

Reorder the terms for easier multiplication:
3 * 4b(3 + b) + 8 = 4(b + 8)

Multiply 3 * 4
12b(3 + b) + 8 = 4(b + 8)
(3 * 12b + b * 12b) + 8 = 4(b + 8)
(36b + 12b2) + 8 = 4(b + 8)

Reorder the terms:
8 + 36b + 12b2 = 4(b + 8)

Reorder the terms:
8 + 36b + 12b2 = 4(8 + b)
8 + 36b + 12b2 = (8 * 4 + b * 4)
8 + 36b + 12b2 = (32 + 4b)

Solving
8 + 36b + 12b2 = 32 + 4b

Solving for variable 'b'.

Reorder the terms:
8 + -32 + 36b + -4b + 12b2 = 32 + 4b + -32 + -4b

Combine like terms: 8 + -32 = -24
-24 + 36b + -4b + 12b2 = 32 + 4b + -32 + -4b

Combine like terms: 36b + -4b = 32b
-24 + 32b + 12b2 = 32 + 4b + -32 + -4b

Reorder the terms:
-24 + 32b + 12b2 = 32 + -32 + 4b + -4b

Combine like terms: 32 + -32 = 0
-24 + 32b + 12b2 = 0 + 4b + -4b
-24 + 32b + 12b2 = 4b + -4b

Combine like terms: 4b + -4b = 0
-24 + 32b + 12b2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + 8b + 3b2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-6 + 8b + 3b2)' equal to zero and attempt to solve:

Simplifying
-6 + 8b + 3b2 = 0

Solving
-6 + 8b + 3b2 = 0

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

Divide each side by '3'.
-2 + 2.666666667b + b2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 2.666666667b + 2 + b2 = 0 + 2

Reorder the terms:
-2 + 2 + 2.666666667b + b2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 2.666666667b + b2 = 0 + 2
2.666666667b + b2 = 0 + 2

Combine like terms: 0 + 2 = 2
2.666666667b + b2 = 2

The b term is 2.666666667b.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667b + 1.777777780 + b2 = 2 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667b + b2 = 2 + 1.777777780

Combine like terms: 2 + 1.777777780 = 3.77777778
1.777777780 + 2.666666667b + b2 = 3.77777778

Factor a perfect square on the left side:
(b + 1.333333334)(b + 1.333333334) = 3.77777778

Calculate the square root of the right side: 1.943650632

Break this problem into two subproblems by setting 
(b + 1.333333334) equal to 1.943650632 and -1.943650632.

Subproblem 1
b + 1.333333334 = 1.943650632

Simplifying
b + 1.333333334 = 1.943650632

Reorder the terms:
1.333333334 + b = 1.943650632

Solving
1.333333334 + b = 1.943650632

Solving for variable 'b'.

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

Add '-1.333333334' to each side of the equation.
1.333333334 + -1.333333334 + b = 1.943650632 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + b = 1.943650632 + -1.333333334
b = 1.943650632 + -1.333333334

Combine like terms: 1.943650632 + -1.333333334 = 0.610317298
b = 0.610317298

Simplifying
b = 0.610317298

Subproblem 2
b + 1.333333334 = -1.943650632

Simplifying
b + 1.333333334 = -1.943650632

Reorder the terms:
1.333333334 + b = -1.943650632

Solving
1.333333334 + b = -1.943650632

Solving for variable 'b'.

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

Add '-1.333333334' to each side of the equation.
1.333333334 + -1.333333334 + b = -1.943650632 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + b = -1.943650632 + -1.333333334
b = -1.943650632 + -1.333333334

Combine like terms: -1.943650632 + -1.333333334 = -3.276983966
b = -3.276983966

Simplifying
b = -3.276983966

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {0.610317298, -3.276983966}
Solution
b = {0.610317298, -3.276983966}