b^2-82b+1677=0

Solution for b^2-82b+1677=0 equation:

Simplifying
b2 + -82b + 1677 = 0

Reorder the terms:
1677 + -82b + b2 = 0

Solving
1677 + -82b + b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(39 + -1b)(43 + -1b) = 0

Subproblem 1
Set the factor '(39 + -1b)' equal to zero and attempt to solve:

Simplifying
39 + -1b = 0

Solving
39 + -1b = 0

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

Add '-39' to each side of the equation.
39 + -39 + -1b = 0 + -39

Combine like terms: 39 + -39 = 0
0 + -1b = 0 + -39
-1b = 0 + -39

Combine like terms: 0 + -39 = -39
-1b = -39

Divide each side by '-1'.
b = 39

Simplifying
b = 39
Subproblem 2
Set the factor '(43 + -1b)' equal to zero and attempt to solve:

Simplifying
43 + -1b = 0

Solving
43 + -1b = 0

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

Add '-43' to each side of the equation.
43 + -43 + -1b = 0 + -43

Combine like terms: 43 + -43 = 0
0 + -1b = 0 + -43
-1b = 0 + -43

Combine like terms: 0 + -43 = -43
-1b = -43

Divide each side by '-1'.
b = 43

Simplifying
b = 43
Solution
b = {39, 43}