(13b-2)(-12b+4)=-4

Solution for (13b-2)(-12b+4)=-4 equation:

Simplifying
(13b + -2)(-12b + 4) = -4

Reorder the terms:
(-2 + 13b)(-12b + 4) = -4

Reorder the terms:
(-2 + 13b)(4 + -12b) = -4

Multiply (-2 + 13b) * (4 + -12b)
(-2(4 + -12b) + 13b * (4 + -12b)) = -4
((4 * -2 + -12b * -2) + 13b * (4 + -12b)) = -4
((-8 + 24b) + 13b * (4 + -12b)) = -4
(-8 + 24b + (4 * 13b + -12b * 13b)) = -4
(-8 + 24b + (52b + -156b2)) = -4

Combine like terms: 24b + 52b = 76b
(-8 + 76b + -156b2) = -4

Solving
-8 + 76b + -156b2 = -4

Solving for variable 'b'.

Reorder the terms:
-8 + 4 + 76b + -156b2 = -4 + 4

Combine like terms: -8 + 4 = -4
-4 + 76b + -156b2 = -4 + 4

Combine like terms: -4 + 4 = 0
-4 + 76b + -156b2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + 19b + -39b2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-1 + 19b + -39b2)' equal to zero and attempt to solve:

Simplifying
-1 + 19b + -39b2 = 0

Solving
-1 + 19b + -39b2 = 0

Begin completing the square.  Divide all terms by
-39 the coefficient of the squared term: 

Divide each side by '-39'.
0.02564102564 + -0.4871794872b + b2 = 0

Move the constant term to the right:

Add '-0.02564102564' to each side of the equation.
0.02564102564 + -0.4871794872b + -0.02564102564 + b2 = 0 + -0.02564102564

Reorder the terms:
0.02564102564 + -0.02564102564 + -0.4871794872b + b2 = 0 + -0.02564102564

Combine like terms: 0.02564102564 + -0.02564102564 = 0.00000000000
0.00000000000 + -0.4871794872b + b2 = 0 + -0.02564102564
-0.4871794872b + b2 = 0 + -0.02564102564

Combine like terms: 0 + -0.02564102564 = -0.02564102564
-0.4871794872b + b2 = -0.02564102564

The b term is -0.4871794872b.  Take half its coefficient (-0.2435897436).
Square it (0.05933596319) and add it to both sides.

Add '0.05933596319' to each side of the equation.
-0.4871794872b + 0.05933596319 + b2 = -0.02564102564 + 0.05933596319

Reorder the terms:
0.05933596319 + -0.4871794872b + b2 = -0.02564102564 + 0.05933596319

Combine like terms: -0.02564102564 + 0.05933596319 = 0.03369493755
0.05933596319 + -0.4871794872b + b2 = 0.03369493755

Factor a perfect square on the left side:
(b + -0.2435897436)(b + -0.2435897436) = 0.03369493755

Calculate the square root of the right side: 0.183561809

Break this problem into two subproblems by setting 
(b + -0.2435897436) equal to 0.183561809 and -0.183561809.

Subproblem 1
b + -0.2435897436 = 0.183561809

Simplifying
b + -0.2435897436 = 0.183561809

Reorder the terms:
-0.2435897436 + b = 0.183561809

Solving
-0.2435897436 + b = 0.183561809

Solving for variable 'b'.

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

Add '0.2435897436' to each side of the equation.
-0.2435897436 + 0.2435897436 + b = 0.183561809 + 0.2435897436

Combine like terms: -0.2435897436 + 0.2435897436 = 0.0000000000
0.0000000000 + b = 0.183561809 + 0.2435897436
b = 0.183561809 + 0.2435897436

Combine like terms: 0.183561809 + 0.2435897436 = 0.4271515526
b = 0.4271515526

Simplifying
b = 0.4271515526

Subproblem 2
b + -0.2435897436 = -0.183561809

Simplifying
b + -0.2435897436 = -0.183561809

Reorder the terms:
-0.2435897436 + b = -0.183561809

Solving
-0.2435897436 + b = -0.183561809

Solving for variable 'b'.

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

Add '0.2435897436' to each side of the equation.
-0.2435897436 + 0.2435897436 + b = -0.183561809 + 0.2435897436

Combine like terms: -0.2435897436 + 0.2435897436 = 0.0000000000
0.0000000000 + b = -0.183561809 + 0.2435897436
b = -0.183561809 + 0.2435897436

Combine like terms: -0.183561809 + 0.2435897436 = 0.0600279346
b = 0.0600279346

Simplifying
b = 0.0600279346

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {0.4271515526, 0.0600279346}
Solution
b = {0.4271515526, 0.0600279346}