27b^2+45b+12=0

Solution for 27b^2+45b+12=0 equation:

Simplifying
27b2 + 45b + 12 = 0

Reorder the terms:
12 + 45b + 27b2 = 0

Solving
12 + 45b + 27b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + 15b + 9b2) = 0

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

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

Simplifying
4 + 3b = 0

Solving
4 + 3b = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3b = 0 + -4

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

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

Divide each side by '3'.
b = -1.333333333

Simplifying
b = -1.333333333
Subproblem 2
Set the factor '(1 + 3b)' equal to zero and attempt to solve:

Simplifying
1 + 3b = 0

Solving
1 + 3b = 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 + 3b = 0 + -1

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

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

Divide each side by '3'.
b = -0.3333333333

Simplifying
b = -0.3333333333
Solution
b = {-1.333333333, -0.3333333333}