12b^2-3b-15=0

Solution for 12b^2-3b-15=0 equation:

Simplifying
12b2 + -3b + -15 = 0

Reorder the terms:
-15 + -3b + 12b2 = 0

Solving
-15 + -3b + 12b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + -1b + 4b2) = 0

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

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

Simplifying
-1 + -1b = 0

Solving
-1 + -1b = 0

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

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

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

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

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

Simplifying
b = -1
Subproblem 2
Set the factor '(5 + -4b)' equal to zero and attempt to solve:

Simplifying
5 + -4b = 0

Solving
5 + -4b = 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 + -4b = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4b = 0 + -5
-4b = 0 + -5

Combine like terms: 0 + -5 = -5
-4b = -5

Divide each side by '-4'.
b = 1.25

Simplifying
b = 1.25
Solution
b = {-1, 1.25}