So I'm trying to find x^13 and x^14 in (4x^3-(1/x))^24

I've done:

(24)

(k) (4x^3)^K (-1/x)^(24-K)

(24)

(k) 4^Kx^3K (-1)^(24-k) x^(K-24)

(24)

(k) 4^K (-1)^(24-K) x^(3K+K-24)

(24)

(K) 4^K (-1)^(24-K) x^(4K-24)

and so for the 13th coefficient, 13 = 4K-24

which is 4K=37, but there's no integer answer for K? I'm sure this is wrong, please help!

PS at the start of each line the 24 and the K are together (ie in two brackets, I'm sure you'll get it)