5-3(b+2)=(2b+7)6(b-12)

Solution for 5-3(b+2)=(2b+7)6(b-12) equation:

Simplifying
5 + -3(b + 2) = (2b + 7) * 6(b + -12)

Reorder the terms:
5 + -3(2 + b) = (2b + 7) * 6(b + -12)
5 + (2 * -3 + b * -3) = (2b + 7) * 6(b + -12)
5 + (-6 + -3b) = (2b + 7) * 6(b + -12)

Combine like terms: 5 + -6 = -1
-1 + -3b = (2b + 7) * 6(b + -12)

Reorder the terms:
-1 + -3b = (7 + 2b) * 6(b + -12)

Reorder the terms:
-1 + -3b = (7 + 2b) * 6(-12 + b)

Reorder the terms for easier multiplication:
-1 + -3b = 6(7 + 2b)(-12 + b)

Multiply (7 + 2b) * (-12 + b)
-1 + -3b = 6(7(-12 + b) + 2b * (-12 + b))
-1 + -3b = 6((-12 * 7 + b * 7) + 2b * (-12 + b))
-1 + -3b = 6((-84 + 7b) + 2b * (-12 + b))
-1 + -3b = 6(-84 + 7b + (-12 * 2b + b * 2b))
-1 + -3b = 6(-84 + 7b + (-24b + 2b2))

Combine like terms: 7b + -24b = -17b
-1 + -3b = 6(-84 + -17b + 2b2)
-1 + -3b = (-84 * 6 + -17b * 6 + 2b2 * 6)
-1 + -3b = (-504 + -102b + 12b2)

Solving
-1 + -3b = -504 + -102b + 12b2

Solving for variable 'b'.

Reorder the terms:
-1 + 504 + -3b + 102b + -12b2 = -504 + -102b + 12b2 + 504 + 102b + -12b2

Combine like terms: -1 + 504 = 503
503 + -3b + 102b + -12b2 = -504 + -102b + 12b2 + 504 + 102b + -12b2

Combine like terms: -3b + 102b = 99b
503 + 99b + -12b2 = -504 + -102b + 12b2 + 504 + 102b + -12b2

Reorder the terms:
503 + 99b + -12b2 = -504 + 504 + -102b + 102b + 12b2 + -12b2

Combine like terms: -504 + 504 = 0
503 + 99b + -12b2 = 0 + -102b + 102b + 12b2 + -12b2
503 + 99b + -12b2 = -102b + 102b + 12b2 + -12b2

Combine like terms: -102b + 102b = 0
503 + 99b + -12b2 = 0 + 12b2 + -12b2
503 + 99b + -12b2 = 12b2 + -12b2

Combine like terms: 12b2 + -12b2 = 0
503 + 99b + -12b2 = 0

Begin completing the square.  Divide all terms by
-12 the coefficient of the squared term: 

Divide each side by '-12'.
-41.91666667 + -8.25b + b2 = 0

Move the constant term to the right:

Add '41.91666667' to each side of the equation.
-41.91666667 + -8.25b + 41.91666667 + b2 = 0 + 41.91666667

Reorder the terms:
-41.91666667 + 41.91666667 + -8.25b + b2 = 0 + 41.91666667

Combine like terms: -41.91666667 + 41.91666667 = 0.00000000
0.00000000 + -8.25b + b2 = 0 + 41.91666667
-8.25b + b2 = 0 + 41.91666667

Combine like terms: 0 + 41.91666667 = 41.91666667
-8.25b + b2 = 41.91666667

The b term is -8.25b.  Take half its coefficient (-4.125).
Square it (17.015625) and add it to both sides.

Add '17.015625' to each side of the equation.
-8.25b + 17.015625 + b2 = 41.91666667 + 17.015625

Reorder the terms:
17.015625 + -8.25b + b2 = 41.91666667 + 17.015625

Combine like terms: 41.91666667 + 17.015625 = 58.93229167
17.015625 + -8.25b + b2 = 58.93229167

Factor a perfect square on the left side:
(b + -4.125)(b + -4.125) = 58.93229167

Calculate the square root of the right side: 7.676737046

Break this problem into two subproblems by setting 
(b + -4.125) equal to 7.676737046 and -7.676737046.

Subproblem 1
b + -4.125 = 7.676737046

Simplifying
b + -4.125 = 7.676737046

Reorder the terms:
-4.125 + b = 7.676737046

Solving
-4.125 + b = 7.676737046

Solving for variable 'b'.

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

Add '4.125' to each side of the equation.
-4.125 + 4.125 + b = 7.676737046 + 4.125

Combine like terms: -4.125 + 4.125 = 0.000
0.000 + b = 7.676737046 + 4.125
b = 7.676737046 + 4.125

Combine like terms: 7.676737046 + 4.125 = 11.801737046
b = 11.801737046

Simplifying
b = 11.801737046

Subproblem 2
b + -4.125 = -7.676737046

Simplifying
b + -4.125 = -7.676737046

Reorder the terms:
-4.125 + b = -7.676737046

Solving
-4.125 + b = -7.676737046

Solving for variable 'b'.

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

Add '4.125' to each side of the equation.
-4.125 + 4.125 + b = -7.676737046 + 4.125

Combine like terms: -4.125 + 4.125 = 0.000
0.000 + b = -7.676737046 + 4.125
b = -7.676737046 + 4.125

Combine like terms: -7.676737046 + 4.125 = -3.551737046
b = -3.551737046

Simplifying
b = -3.551737046

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {11.801737046, -3.551737046}