2w^2+21w+52=0

Solution for 2w^2+21w+52=0 equation:

Simplifying
2w2 + 21w + 52 = 0

Reorder the terms:
52 + 21w + 2w2 = 0

Solving
52 + 21w + 2w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(13 + 2w)(4 + w) = 0

Subproblem 1
Set the factor '(13 + 2w)' equal to zero and attempt to solve:

Simplifying
13 + 2w = 0

Solving
13 + 2w = 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 + 2w = 0 + -13

Combine like terms: 13 + -13 = 0
0 + 2w = 0 + -13
2w = 0 + -13

Combine like terms: 0 + -13 = -13
2w = -13

Divide each side by '2'.
w = -6.5

Simplifying
w = -6.5
Subproblem 2
Set the factor '(4 + w)' equal to zero and attempt to solve:

Simplifying
4 + w = 0

Solving
4 + w = 0

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

Add '-4' to each side of the equation.
4 + -4 + w = 0 + -4

Combine like terms: 4 + -4 = 0
0 + w = 0 + -4
w = 0 + -4

Combine like terms: 0 + -4 = -4
w = -4

Simplifying
w = -4
Solution
w = {-6.5, -4}