4s^2-62s-32=0

Solution for 4s^2-62s-32=0 equation:

Simplifying
4s2 + -62s + -32 = 0

Reorder the terms:
-32 + -62s + 4s2 = 0

Solving
-32 + -62s + 4s2 = 0

Solving for variable 's'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-16 + -31s + 2s2) = 0

Factor a trinomial.
2((-1 + -2s)(16 + -1s)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(16 + -1s)' equal to zero and attempt to solve:

Simplifying
16 + -1s = 0

Solving
16 + -1s = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1s = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1s = 0 + -16
-1s = 0 + -16

Combine like terms: 0 + -16 = -16
-1s = -16

Divide each side by '-1'.
s = 16

Simplifying
s = 16
Solution
s = {-0.5, 16}