w^2+28w+52=0

Solution for w^2+28w+52=0 equation:

Simplifying
w2 + 28w + 52 = 0

Reorder the terms:
52 + 28w + w2 = 0

Solving
52 + 28w + w2 = 0

Solving for variable 'w'.

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

Subproblem 1
Set the factor '(26 + w)' equal to zero and attempt to solve:

Simplifying
26 + w = 0

Solving
26 + w = 0

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

Add '-26' to each side of the equation.
26 + -26 + w = 0 + -26

Combine like terms: 26 + -26 = 0
0 + w = 0 + -26
w = 0 + -26

Combine like terms: 0 + -26 = -26
w = -26

Simplifying
w = -26
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 = {-26, -2}