(13b+9)(4b-12)=0

Solution for (13b+9)(4b-12)=0 equation:

Simplifying
(13b + 9)(4b + -12) = 0

Reorder the terms:
(9 + 13b)(4b + -12) = 0

Reorder the terms:
(9 + 13b)(-12 + 4b) = 0

Multiply (9 + 13b) * (-12 + 4b)
(9(-12 + 4b) + 13b * (-12 + 4b)) = 0
((-12 * 9 + 4b * 9) + 13b * (-12 + 4b)) = 0
((-108 + 36b) + 13b * (-12 + 4b)) = 0
(-108 + 36b + (-12 * 13b + 4b * 13b)) = 0
(-108 + 36b + (-156b + 52b2)) = 0

Combine like terms: 36b + -156b = -120b
(-108 + -120b + 52b2) = 0

Solving
-108 + -120b + 52b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-27 + -30b + 13b2) = 0

Factor a trinomial.
4((-9 + -13b)(3 + -1b)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-9 + -13b)' equal to zero and attempt to solve:

Simplifying
-9 + -13b = 0

Solving
-9 + -13b = 0

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

Add '9' to each side of the equation.
-9 + 9 + -13b = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -13b = 0 + 9
-13b = 0 + 9

Combine like terms: 0 + 9 = 9
-13b = 9

Divide each side by '-13'.
b = -0.6923076923

Simplifying
b = -0.6923076923
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 = {-0.6923076923, 3}