0=5s^2+6s+1

Solution for 0=5s^2+6s+1 equation:

Simplifying
0 = 5s2 + 6s + 1

Reorder the terms:
0 = 1 + 6s + 5s2

Solving
0 = 1 + 6s + 5s2

Solving for variable 's'.

Combine like terms: 0 + -1 = -1
-1 + -6s + -5s2 = 1 + 6s + 5s2 + -1 + -6s + -5s2

Reorder the terms:
-1 + -6s + -5s2 = 1 + -1 + 6s + -6s + 5s2 + -5s2

Combine like terms: 1 + -1 = 0
-1 + -6s + -5s2 = 0 + 6s + -6s + 5s2 + -5s2
-1 + -6s + -5s2 = 6s + -6s + 5s2 + -5s2

Combine like terms: 6s + -6s = 0
-1 + -6s + -5s2 = 0 + 5s2 + -5s2
-1 + -6s + -5s2 = 5s2 + -5s2

Combine like terms: 5s2 + -5s2 = 0
-1 + -6s + -5s2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 6s + 5s2) = 0

Factor a trinomial.
-1((1 + s)(1 + 5s)) = 0

Ignore the factor -1.
Subproblem 1
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
Subproblem 2
Set the factor '(1 + 5s)' equal to zero and attempt to solve:

Simplifying
1 + 5s = 0

Solving
1 + 5s = 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 + 5s = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5s = 0 + -1
5s = 0 + -1

Combine like terms: 0 + -1 = -1
5s = -1

Divide each side by '5'.
s = -0.2

Simplifying
s = -0.2
Solution
s = {-1, -0.2}