for the implicit integration I got:

the vertical tangent would at points at which y' goes to infinity.
that happen when the right-hand side has singularities, that is, the denominator is 0:

so the two points y above have a vertical tangent.
Add the similar variables (think apple+apple), in this case, we would add 2q+4q.
Well, what is 4 apples plus 2 apples? 6 apples, simply, 6q
Since 3 is without a variable, we will leave it as is
Therefore, 2q+4q+3= 6q+3
Hope this helped :)