(b-3)(3b-1)-2b(b+2)=

Solution for (b-3)(3b-1)-2b(b+2)= equation:

Simplifying
(b + -3)(3b + -1) + -2b(b + 2) = 0

Reorder the terms:
(-3 + b)(3b + -1) + -2b(b + 2) = 0

Reorder the terms:
(-3 + b)(-1 + 3b) + -2b(b + 2) = 0

Multiply (-3 + b) * (-1 + 3b)
(-3(-1 + 3b) + b(-1 + 3b)) + -2b(b + 2) = 0
((-1 * -3 + 3b * -3) + b(-1 + 3b)) + -2b(b + 2) = 0
((3 + -9b) + b(-1 + 3b)) + -2b(b + 2) = 0
(3 + -9b + (-1 * b + 3b * b)) + -2b(b + 2) = 0
(3 + -9b + (-1b + 3b2)) + -2b(b + 2) = 0

Combine like terms: -9b + -1b = -10b
(3 + -10b + 3b2) + -2b(b + 2) = 0

Reorder the terms:
3 + -10b + 3b2 + -2b(2 + b) = 0
3 + -10b + 3b2 + (2 * -2b + b * -2b) = 0
3 + -10b + 3b2 + (-4b + -2b2) = 0

Reorder the terms:
3 + -10b + -4b + 3b2 + -2b2 = 0

Combine like terms: -10b + -4b = -14b
3 + -14b + 3b2 + -2b2 = 0

Combine like terms: 3b2 + -2b2 = 1b2
3 + -14b + 1b2 = 0

Solving
3 + -14b + 1b2 = 0

Solving for variable 'b'.

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -14b + -3 + b2 = 0 + -3

Reorder the terms:
3 + -3 + -14b + b2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -14b + b2 = 0 + -3
-14b + b2 = 0 + -3

Combine like terms: 0 + -3 = -3
-14b + b2 = -3

The b term is -14b.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14b + 49 + b2 = -3 + 49

Reorder the terms:
49 + -14b + b2 = -3 + 49

Combine like terms: -3 + 49 = 46
49 + -14b + b2 = 46

Factor a perfect square on the left side:
(b + -7)(b + -7) = 46

Calculate the square root of the right side: 6.782329983

Break this problem into two subproblems by setting 
(b + -7) equal to 6.782329983 and -6.782329983.

Subproblem 1
b + -7 = 6.782329983

Simplifying
b + -7 = 6.782329983

Reorder the terms:
-7 + b = 6.782329983

Solving
-7 + b = 6.782329983

Solving for variable 'b'.

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

Add '7' to each side of the equation.
-7 + 7 + b = 6.782329983 + 7

Combine like terms: -7 + 7 = 0
0 + b = 6.782329983 + 7
b = 6.782329983 + 7

Combine like terms: 6.782329983 + 7 = 13.782329983
b = 13.782329983

Simplifying
b = 13.782329983

Subproblem 2
b + -7 = -6.782329983

Simplifying
b + -7 = -6.782329983

Reorder the terms:
-7 + b = -6.782329983

Solving
-7 + b = -6.782329983

Solving for variable 'b'.

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

Add '7' to each side of the equation.
-7 + 7 + b = -6.782329983 + 7

Combine like terms: -7 + 7 = 0
0 + b = -6.782329983 + 7
b = -6.782329983 + 7

Combine like terms: -6.782329983 + 7 = 0.217670017
b = 0.217670017

Simplifying
b = 0.217670017

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {13.782329983, 0.217670017}