If you divide both sides of either equation by n you can eliminate all but a few choices for n
(1) (n-1)! = 8n^3 + 15n^2 - 4n^1 + 15 + 8/n
and
(2) (n-1)! = 9n^3 + 4n^2 + n + 1344/n
And knowing that the final term must be an integer limits the possibilties to divisors of 8 for equation 1 and 1355 for equation 2.
For the second equation, n! must be greater than 1344, so n > 6 for that one.
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