-b^2-5b+66=0

Solution for -b^2-5b+66=0 equation:

Simplifying
-1b2 + -5b + 66 = 0

Reorder the terms:
66 + -5b + -1b2 = 0

Solving
66 + -5b + -1b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(6 + -1b)(11 + b) = 0

Subproblem 1
Set the factor '(6 + -1b)' equal to zero and attempt to solve:

Simplifying
6 + -1b = 0

Solving
6 + -1b = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1b = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1b = 0 + -6
-1b = 0 + -6

Combine like terms: 0 + -6 = -6
-1b = -6

Divide each side by '-1'.
b = 6

Simplifying
b = 6
Subproblem 2
Set the factor '(11 + b)' equal to zero and attempt to solve:

Simplifying
11 + b = 0

Solving
11 + b = 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 + b = 0 + -11

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

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

Simplifying
b = -11
Solution
b = {6, -11}