In this particular instance, r can be solved as far as to establish it is equal to -9 + 2st over 6q + 7s. You cannot solve the equation further than this, but the part from this is as follows:
6qr + 7rs - 2st = -9
6qr + 7rs = -9 + 2st
r(6q+7s) = -9 + 2st
if you simplify this down further, you will find the answer mentioned above.