w^2+13w+22=0

Solution for w^2+13w+22=0 equation:

Simplifying
w2 + 13w + 22 = 0

Reorder the terms:
22 + 13w + w2 = 0

Solving
22 + 13w + w2 = 0

Solving for variable 'w'.

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

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

Simplifying
11 + w = 0

Solving
11 + w = 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 + w = 0 + -11

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

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

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

Simplifying
2 + w = 0

Solving
2 + w = 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 + w = 0 + -2

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

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

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