-2s^2-5s-2=0

Solution for -2s^2-5s-2=0 equation:

Simplifying
-2s2 + -5s + -2 = 0

Reorder the terms:
-2 + -5s + -2s2 = 0

Solving
-2 + -5s + -2s2 = 0

Solving for variable 's'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(2 + 5s + 2s2) = 0

Factor a trinomial.
-1((2 + s)(1 + 2s)) = 0

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

Simplifying
2 + s = 0

Solving
2 + s = 0

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

Add '-2' to each side of the equation.
2 + -2 + s = 0 + -2

Combine like terms: 2 + -2 = 0
0 + s = 0 + -2
s = 0 + -2

Combine like terms: 0 + -2 = -2
s = -2

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

Simplifying
1 + 2s = 0

Solving
1 + 2s = 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 + 2s = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2s = 0 + -1
2s = 0 + -1

Combine like terms: 0 + -1 = -1
2s = -1

Divide each side by '2'.
s = -0.5

Simplifying
s = -0.5
Solution
s = {-2, -0.5}