5s+s^2+4=0

Solution for 5s+s^2+4=0 equation:

Simplifying
5s + s2 + 4 = 0

Reorder the terms:
4 + 5s + s2 = 0

Solving
4 + 5s + s2 = 0

Solving for variable 's'.

Factor a trinomial.
(4 + s)(1 + s) = 0

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

Simplifying
1 + s = 0

Solving
1 + s = 0

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

Add '-1' to each side of the equation.
1 + -1 + s = 0 + -1

Combine like terms: 1 + -1 = 0
0 + s = 0 + -1
s = 0 + -1

Combine like terms: 0 + -1 = -1
s = -1

Simplifying
s = -1
Solution
s = {-4, -1}