Arithmetic progressions. "Consider an 4 term arithmetic sequence. The difference is 4, and the product of all four terms is 585. Write the progression".
My way of finding the progression seems like it will take too long, but here it is, anyway:
$$a_1\cdot a_2\cdot a_3\cdot a_4=585$$
$$a_1\cdot (a_1+4)\cdot (a_1+8)\cdot (a_1+12)=585$$
and after some operations
$$a^4 +4a^3+196a^2+384a-585=0 $$
Is there a faster, less frustrating way of solving this? Thanks in advance/

Another way to do it is to factor $585$, which turns out to be
$$3^2\cdot 5\cdot 13$$
And using the factorization, find four factors which each differ by $4$.

 $$1\times 5\times 9\times 13$$

