So I fully realize I need to brush up on my Algebra.. but...

That is not all you have to ensure, unfortunately. That method will find you ONE factor, but not all of them. If you are ever trying to find factors (or values for a particular variable), do NOT divide out the variable you are supposed to solve for - or you will lose a factor (typically zero).

This is a quadratic so we first to set everything equal to zero:
14s=6s^2
0 = 6s^2 - 14s
then, factor out (NOT divide out) an s
0 = s(6s-14)
now set each factor equal to zero
0 = s
0 = 6s-14 => 14 = 6s => 14/6 = s

So 7/3 is one factor, but 0 is also a factor.