17s+s^2+52=0

Solution for 17s+s^2+52=0 equation:

Simplifying
17s + s2 + 52 = 0

Reorder the terms:
52 + 17s + s2 = 0

Solving
52 + 17s + s2 = 0

Solving for variable 's'.

Factor a trinomial.
(13 + s)(4 + s) = 0

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

Simplifying
13 + s = 0

Solving
13 + s = 0

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

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

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

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

Simplifying
s = -13
Subproblem 2
Set the factor '(4 + s)' equal to zero and attempt to solve:

Simplifying
4 + s = 0

Solving
4 + s = 0

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

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

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

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

Simplifying
s = -4
Solution
s = {-13, -4}