We have to have equal to a whole number; and presumably the value(s) of b we are looking for are integers greater than or equal to 2.
Since 9 is a whole number, has to be a whole number also.
So we know b has to be a whole number greater than or equal to 2; and we know 56 has to be divisible by (b+7). The only divisors of 56 that are 9 or greater are 14, 28, and 56.
Since those divisors are the values of (b+7), the three bases for which (b+7) divides into (9b+7) without any remainder are 7, 21, and 49.
