32s^2-4s-1=0

Solution for 32s^2-4s-1=0 equation:

Simplifying
32s2 + -4s + -1 = 0

Reorder the terms:
-1 + -4s + 32s2 = 0

Solving
-1 + -4s + 32s2 = 0

Solving for variable 's'.

Factor a trinomial.
(-1 + -8s)(1 + -4s) = 0

Subproblem 1
Set the factor '(-1 + -8s)' equal to zero and attempt to solve:

Simplifying
-1 + -8s = 0

Solving
-1 + -8s = 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 + -8s = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -8s = 0 + 1
-8s = 0 + 1

Combine like terms: 0 + 1 = 1
-8s = 1

Divide each side by '-8'.
s = -0.125

Simplifying
s = -0.125
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 = {-0.125, 0.25}