w^2-18w-19=0

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

Simplifying
w2 + -18w + -19 = 0

Reorder the terms:
-19 + -18w + w2 = 0

Solving
-19 + -18w + w2 = 0

Solving for variable 'w'.

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

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

Simplifying
-1 + -1w = 0

Solving
-1 + -1w = 0

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

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

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

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

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

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

Simplifying
19 + -1w = 0

Solving
19 + -1w = 0

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

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

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

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

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

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