(9b+5)(4b-12)=0

Solution for (9b+5)(4b-12)=0 equation:

Simplifying
(9b + 5)(4b + -12) = 0

Reorder the terms:
(5 + 9b)(4b + -12) = 0

Reorder the terms:
(5 + 9b)(-12 + 4b) = 0

Multiply (5 + 9b) * (-12 + 4b)
(5(-12 + 4b) + 9b * (-12 + 4b)) = 0
((-12 * 5 + 4b * 5) + 9b * (-12 + 4b)) = 0
((-60 + 20b) + 9b * (-12 + 4b)) = 0
(-60 + 20b + (-12 * 9b + 4b * 9b)) = 0
(-60 + 20b + (-108b + 36b2)) = 0

Combine like terms: 20b + -108b = -88b
(-60 + -88b + 36b2) = 0

Solving
-60 + -88b + 36b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-15 + -22b + 9b2) = 0

Factor a trinomial.
4((-5 + -9b)(3 + -1b)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-5 + -9b)' equal to zero and attempt to solve:

Simplifying
-5 + -9b = 0

Solving
-5 + -9b = 0

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

Add '5' to each side of the equation.
-5 + 5 + -9b = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -9b = 0 + 5
-9b = 0 + 5

Combine like terms: 0 + 5 = 5
-9b = 5

Divide each side by '-9'.
b = -0.5555555556

Simplifying
b = -0.5555555556
Subproblem 2
Set the factor '(3 + -1b)' equal to zero and attempt to solve:

Simplifying
3 + -1b = 0

Solving
3 + -1b = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1b = 0 + -3
-1b = 0 + -3

Combine like terms: 0 + -3 = -3
-1b = -3

Divide each side by '-1'.
b = 3

Simplifying
b = 3
Solution
b = {-0.5555555556, 3}