4s^2+45s+11=0

Solution for 4s^2+45s+11=0 equation:

Simplifying
4s2 + 45s + 11 = 0

Reorder the terms:
11 + 45s + 4s2 = 0

Solving
11 + 45s + 4s2 = 0

Solving for variable 's'.

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

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

Simplifying
11 + s = 0

Solving
11 + s = 0

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

Add '-11' to each side of the equation.
11 + -11 + s = 0 + -11

Combine like terms: 11 + -11 = 0
0 + s = 0 + -11
s = 0 + -11

Combine like terms: 0 + -11 = -11
s = -11

Simplifying
s = -11
Subproblem 2
Set the factor '(1 + 4s)' equal to zero and attempt to solve:

Simplifying
1 + 4s = 0

Solving
1 + 4s = 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 + 4s = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4s = 0 + -1
4s = 0 + -1

Combine like terms: 0 + -1 = -1
4s = -1

Divide each side by '4'.
s = -0.25

Simplifying
s = -0.25
Solution
s = {-11, -0.25}