(5b-3)(2b-6)-(-3+8b)(4b-4)=

Solution for (5b-3)(2b-6)-(-3+8b)(4b-4)= equation:

Simplifying
(5b + -3)(2b + -6) + -1(-3 + 8b)(4b + -4) = 0

Reorder the terms:
(-3 + 5b)(2b + -6) + -1(-3 + 8b)(4b + -4) = 0

Reorder the terms:
(-3 + 5b)(-6 + 2b) + -1(-3 + 8b)(4b + -4) = 0

Multiply (-3 + 5b) * (-6 + 2b)
(-3(-6 + 2b) + 5b * (-6 + 2b)) + -1(-3 + 8b)(4b + -4) = 0
((-6 * -3 + 2b * -3) + 5b * (-6 + 2b)) + -1(-3 + 8b)(4b + -4) = 0
((18 + -6b) + 5b * (-6 + 2b)) + -1(-3 + 8b)(4b + -4) = 0
(18 + -6b + (-6 * 5b + 2b * 5b)) + -1(-3 + 8b)(4b + -4) = 0
(18 + -6b + (-30b + 10b2)) + -1(-3 + 8b)(4b + -4) = 0

Combine like terms: -6b + -30b = -36b
(18 + -36b + 10b2) + -1(-3 + 8b)(4b + -4) = 0

Reorder the terms:
18 + -36b + 10b2 + -1(-3 + 8b)(-4 + 4b) = 0

Multiply (-3 + 8b) * (-4 + 4b)
18 + -36b + 10b2 + -1(-3(-4 + 4b) + 8b * (-4 + 4b)) = 0
18 + -36b + 10b2 + -1((-4 * -3 + 4b * -3) + 8b * (-4 + 4b)) = 0
18 + -36b + 10b2 + -1((12 + -12b) + 8b * (-4 + 4b)) = 0
18 + -36b + 10b2 + -1(12 + -12b + (-4 * 8b + 4b * 8b)) = 0
18 + -36b + 10b2 + -1(12 + -12b + (-32b + 32b2)) = 0

Combine like terms: -12b + -32b = -44b
18 + -36b + 10b2 + -1(12 + -44b + 32b2) = 0
18 + -36b + 10b2 + (12 * -1 + -44b * -1 + 32b2 * -1) = 0
18 + -36b + 10b2 + (-12 + 44b + -32b2) = 0

Reorder the terms:
18 + -12 + -36b + 44b + 10b2 + -32b2 = 0

Combine like terms: 18 + -12 = 6
6 + -36b + 44b + 10b2 + -32b2 = 0

Combine like terms: -36b + 44b = 8b
6 + 8b + 10b2 + -32b2 = 0

Combine like terms: 10b2 + -32b2 = -22b2
6 + 8b + -22b2 = 0

Solving
6 + 8b + -22b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 4b + -11b2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + 4b + -11b2)' equal to zero and attempt to solve:

Simplifying
3 + 4b + -11b2 = 0

Solving
3 + 4b + -11b2 = 0

Begin completing the square.  Divide all terms by
-11 the coefficient of the squared term: 

Divide each side by '-11'.
-0.2727272727 + -0.3636363636b + b2 = 0

Move the constant term to the right:

Add '0.2727272727' to each side of the equation.
-0.2727272727 + -0.3636363636b + 0.2727272727 + b2 = 0 + 0.2727272727

Reorder the terms:
-0.2727272727 + 0.2727272727 + -0.3636363636b + b2 = 0 + 0.2727272727

Combine like terms: -0.2727272727 + 0.2727272727 = 0.0000000000
0.0000000000 + -0.3636363636b + b2 = 0 + 0.2727272727
-0.3636363636b + b2 = 0 + 0.2727272727

Combine like terms: 0 + 0.2727272727 = 0.2727272727
-0.3636363636b + b2 = 0.2727272727

The b term is -0.3636363636b.  Take half its coefficient (-0.1818181818).
Square it (0.03305785123) and add it to both sides.

Add '0.03305785123' to each side of the equation.
-0.3636363636b + 0.03305785123 + b2 = 0.2727272727 + 0.03305785123

Reorder the terms:
0.03305785123 + -0.3636363636b + b2 = 0.2727272727 + 0.03305785123

Combine like terms: 0.2727272727 + 0.03305785123 = 0.30578512393
0.03305785123 + -0.3636363636b + b2 = 0.30578512393

Factor a perfect square on the left side:
(b + -0.1818181818)(b + -0.1818181818) = 0.30578512393

Calculate the square root of the right side: 0.552978412

Break this problem into two subproblems by setting 
(b + -0.1818181818) equal to 0.552978412 and -0.552978412.

Subproblem 1
b + -0.1818181818 = 0.552978412

Simplifying
b + -0.1818181818 = 0.552978412

Reorder the terms:
-0.1818181818 + b = 0.552978412

Solving
-0.1818181818 + b = 0.552978412

Solving for variable 'b'.

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

Add '0.1818181818' to each side of the equation.
-0.1818181818 + 0.1818181818 + b = 0.552978412 + 0.1818181818

Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000
0.0000000000 + b = 0.552978412 + 0.1818181818
b = 0.552978412 + 0.1818181818

Combine like terms: 0.552978412 + 0.1818181818 = 0.7347965938
b = 0.7347965938

Simplifying
b = 0.7347965938

Subproblem 2
b + -0.1818181818 = -0.552978412

Simplifying
b + -0.1818181818 = -0.552978412

Reorder the terms:
-0.1818181818 + b = -0.552978412

Solving
-0.1818181818 + b = -0.552978412

Solving for variable 'b'.

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

Add '0.1818181818' to each side of the equation.
-0.1818181818 + 0.1818181818 + b = -0.552978412 + 0.1818181818

Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000
0.0000000000 + b = -0.552978412 + 0.1818181818
b = -0.552978412 + 0.1818181818

Combine like terms: -0.552978412 + 0.1818181818 = -0.3711602302
b = -0.3711602302

Simplifying
b = -0.3711602302

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {0.7347965938, -0.3711602302}
Solution
b = {0.7347965938, -0.3711602302}