-b^2-8b+33=0

Solution for -b^2-8b+33=0 equation:

Simplifying
-1b2 + -8b + 33 = 0

Reorder the terms:
33 + -8b + -1b2 = 0

Solving
33 + -8b + -1b2 = 0

Solving for variable 'b'.

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

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

Simplifying
3 + -1b = 0

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

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

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

Divide each side by '-1'.
b = 3

Simplifying
b = 3
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 = {3, -11}