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/

The faster way of doing this would be to let your product be $(a - 6)(a-2)(a+2)(a+6) = 585$. This then expands to $(a^2 - 4)(a^2 - 36) = 585$, which substituting $b = a^2$ yields a quadratic which can be more easily factored. 

 You end up getting $a^2 = 49$ as the only positive root, so you have $a = 7$ and your 
 sequence is:
 $1, 5, 9, 13$. 

