w^2+21w=-104

Solution for w^2+21w=-104 equation:

Simplifying
w2 + 21w = -104

Reorder the terms:
21w + w2 = -104

Solving
21w + w2 = -104

Solving for variable 'w'.

Reorder the terms:
104 + 21w + w2 = -104 + 104

Combine like terms: -104 + 104 = 0
104 + 21w + w2 = 0

Factor a trinomial.
(13 + w)(8 + w) = 0

Subproblem 1
Set the factor '(13 + w)' equal to zero and attempt to solve:

Simplifying
13 + w = 0

Solving
13 + w = 0

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

Add '-13' to each side of the equation.
13 + -13 + w = 0 + -13

Combine like terms: 13 + -13 = 0
0 + w = 0 + -13
w = 0 + -13

Combine like terms: 0 + -13 = -13
w = -13

Simplifying
w = -13
Subproblem 2
Set the factor '(8 + w)' equal to zero and attempt to solve:

Simplifying
8 + w = 0

Solving
8 + w = 0

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

Add '-8' to each side of the equation.
8 + -8 + w = 0 + -8

Combine like terms: 8 + -8 = 0
0 + w = 0 + -8
w = 0 + -8

Combine like terms: 0 + -8 = -8
w = -8

Simplifying
w = -8
Solution
w = {-13, -8}