Answer: -3060
68
-45
--------
340
272x <-- the x is in place of a zero
--------
3060
times the negative: -3060
By either long or synthetic division, it's easy to show that

The quartic will be exactly divisible by

when the numerator of the remainder term vanishes, or for those values of

such that

I'm not sure how to count the number of solutions (software tells me it should be 80), but hopefully this is a helpful push in the right direction.
The equation has one solution, x = -7.