3b^2-27b-66=0

Solution for 3b^2-27b-66=0 equation:

Simplifying
3b2 + -27b + -66 = 0

Reorder the terms:
-66 + -27b + 3b2 = 0

Solving
-66 + -27b + 3b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-22 + -9b + b2) = 0

Factor a trinomial.
3((-2 + -1b)(11 + -1b)) = 0

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

Simplifying
-2 + -1b = 0

Solving
-2 + -1b = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1b = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1b = 0 + 2
-1b = 0 + 2

Combine like terms: 0 + 2 = 2
-1b = 2

Divide each side by '-1'.
b = -2

Simplifying
b = -2
Subproblem 2
Set the factor '(11 + -1b)' equal to zero and attempt to solve:

Simplifying
11 + -1b = 0

Solving
11 + -1b = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1b = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1b = 0 + -11
-1b = 0 + -11

Combine like terms: 0 + -11 = -11
-1b = -11

Divide each side by '-1'.
b = 11

Simplifying
b = 11
Solution
b = {-2, 11}