12b^2-51b-45=0

Solution for 12b^2-51b-45=0 equation:

Simplifying
12b2 + -51b + -45 = 0

Reorder the terms:
-45 + -51b + 12b2 = 0

Solving
-45 + -51b + 12b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-15 + -17b + 4b2) = 0

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

Ignore the factor 3.
Subproblem 1
Set the factor '(-3 + -4b)' equal to zero and attempt to solve:

Simplifying
-3 + -4b = 0

Solving
-3 + -4b = 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 + -4b = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4b = 0 + 3
-4b = 0 + 3

Combine like terms: 0 + 3 = 3
-4b = 3

Divide each side by '-4'.
b = -0.75

Simplifying
b = -0.75
Subproblem 2
Set the factor '(5 + -1b)' equal to zero and attempt to solve:

Simplifying
5 + -1b = 0

Solving
5 + -1b = 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 + -1b = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1b = 0 + -5
-1b = 0 + -5

Combine like terms: 0 + -5 = -5
-1b = -5

Divide each side by '-1'.
b = 5

Simplifying
b = 5
Solution
b = {-0.75, 5}