(8b-12)(2b+5)=180

Solution for (8b-12)(2b+5)=180 equation:

Simplifying
(8b + -12)(2b + 5) = 180

Reorder the terms:
(-12 + 8b)(2b + 5) = 180

Reorder the terms:
(-12 + 8b)(5 + 2b) = 180

Multiply (-12 + 8b) * (5 + 2b)
(-12(5 + 2b) + 8b * (5 + 2b)) = 180
((5 * -12 + 2b * -12) + 8b * (5 + 2b)) = 180
((-60 + -24b) + 8b * (5 + 2b)) = 180
(-60 + -24b + (5 * 8b + 2b * 8b)) = 180
(-60 + -24b + (40b + 16b2)) = 180

Combine like terms: -24b + 40b = 16b
(-60 + 16b + 16b2) = 180

Solving
-60 + 16b + 16b2 = 180

Solving for variable 'b'.

Reorder the terms:
-60 + -180 + 16b + 16b2 = 180 + -180

Combine like terms: -60 + -180 = -240
-240 + 16b + 16b2 = 180 + -180

Combine like terms: 180 + -180 = 0
-240 + 16b + 16b2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(-15 + b + b2) = 0

Ignore the factor 16.
Subproblem 1
Set the factor '(-15 + b + b2)' equal to zero and attempt to solve:

Simplifying
-15 + b + b2 = 0

Solving
-15 + b + b2 = 0

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + b + 15 + b2 = 0 + 15

Reorder the terms:
-15 + 15 + b + b2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + b + b2 = 0 + 15
b + b2 = 0 + 15

Combine like terms: 0 + 15 = 15
b + b2 = 15

The b term is b.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
b + 0.25 + b2 = 15 + 0.25

Reorder the terms:
0.25 + b + b2 = 15 + 0.25

Combine like terms: 15 + 0.25 = 15.25
0.25 + b + b2 = 15.25

Factor a perfect square on the left side:
(b + 0.5)(b + 0.5) = 15.25

Calculate the square root of the right side: 3.905124838

Break this problem into two subproblems by setting 
(b + 0.5) equal to 3.905124838 and -3.905124838.

Subproblem 1
b + 0.5 = 3.905124838

Simplifying
b + 0.5 = 3.905124838

Reorder the terms:
0.5 + b = 3.905124838

Solving
0.5 + b = 3.905124838

Solving for variable 'b'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + b = 3.905124838 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + b = 3.905124838 + -0.5
b = 3.905124838 + -0.5

Combine like terms: 3.905124838 + -0.5 = 3.405124838
b = 3.405124838

Simplifying
b = 3.405124838

Subproblem 2
b + 0.5 = -3.905124838

Simplifying
b + 0.5 = -3.905124838

Reorder the terms:
0.5 + b = -3.905124838

Solving
0.5 + b = -3.905124838

Solving for variable 'b'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + b = -3.905124838 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + b = -3.905124838 + -0.5
b = -3.905124838 + -0.5

Combine like terms: -3.905124838 + -0.5 = -4.405124838
b = -4.405124838

Simplifying
b = -4.405124838

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {3.405124838, -4.405124838}
Solution
b = {3.405124838, -4.405124838}