2w^2+21w+55=0

Solution for 2w^2+21w+55=0 equation:

Simplifying
2w2 + 21w + 55 = 0

Reorder the terms:
55 + 21w + 2w2 = 0

Solving
55 + 21w + 2w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(11 + 2w)(5 + w) = 0

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

Simplifying
11 + 2w = 0

Solving
11 + 2w = 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 + 2w = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 2w = 0 + -11
2w = 0 + -11

Combine like terms: 0 + -11 = -11
2w = -11

Divide each side by '2'.
w = -5.5

Simplifying
w = -5.5
Subproblem 2
Set the factor '(5 + w)' equal to zero and attempt to solve:

Simplifying
5 + w = 0

Solving
5 + w = 0

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

Add '-5' to each side of the equation.
5 + -5 + w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + w = 0 + -5
w = 0 + -5

Combine like terms: 0 + -5 = -5
w = -5

Simplifying
w = -5
Solution
w = {-5.5, -5}