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 + b)(5 + 4b)) = 0

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

Simplifying
3 + b = 0

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

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

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

Simplifying
b = -3
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 = {-3, -1.25}