w^2-9w-22=0

Solution for w^2-9w-22=0 equation:

Simplifying
w2 + -9w + -22 = 0

Reorder the terms:
-22 + -9w + w2 = 0

Solving
-22 + -9w + w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-2 + -1w)(11 + -1w) = 0

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

Simplifying
-2 + -1w = 0

Solving
-2 + -1w = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1w = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1w = 0 + 2
-1w = 0 + 2

Combine like terms: 0 + 2 = 2
-1w = 2

Divide each side by '-1'.
w = -2

Simplifying
w = -2
Subproblem 2
Set the factor '(11 + -1w)' equal to zero and attempt to solve:

Simplifying
11 + -1w = 0

Solving
11 + -1w = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1w = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1w = 0 + -11
-1w = 0 + -11

Combine like terms: 0 + -11 = -11
-1w = -11

Divide each side by '-1'.
w = 11

Simplifying
w = 11
Solution
w = {-2, 11}