Assuming b is an integer, we first look at factors of 4, being 1 and 4 or 2 and 2. The factors of 3 are 1 and 3 only. So the factorisation possibilities are (x+3)(4x+1), (4x+3)(x+1) and (2x+1)(2x+3).
Expanding these we get: 4x²+13x+3, 4x²+7x+3 and 4x²+8x+3, giving values of b=13, 7 and 8.
(Other rational values of b exist but they are not integers.)