b^2-18b-19=0

Solution for b^2-18b-19=0 equation:

Simplifying
b2 + -18b + -19 = 0

Reorder the terms:
-19 + -18b + b2 = 0

Solving
-19 + -18b + b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-1 + -1b)(19 + -1b) = 0

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

Simplifying
-1 + -1b = 0

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

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

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

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

Simplifying
b = -1
Subproblem 2
Set the factor '(19 + -1b)' equal to zero and attempt to solve:

Simplifying
19 + -1b = 0

Solving
19 + -1b = 0

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

Add '-19' to each side of the equation.
19 + -19 + -1b = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -1b = 0 + -19
-1b = 0 + -19

Combine like terms: 0 + -19 = -19
-1b = -19

Divide each side by '-1'.
b = 19

Simplifying
b = 19
Solution
b = {-1, 19}