TITLE: Solve $(4x+3)^2(2x+1)(x+1)=75$?
QUESTION [5 upvotes]: How do I find in set of complex numbers the solutions of the following equation?
$$(4x+3)^2(2x+1)(x+1)=75$$
I hope you'll give me just a hint.
Thank you very much!

REPLY [5 votes]: We note that $75=5^2\times 3$
Hence, we try to see whether we can be lucky to have integer solutions. Setiing $4x+3=\pm5$ gives $2$ values for $x$,i.e. $x=1/2,-2$ for which above equation is satisfied. 
Now you can divide to get a quadratic and get other $2$ roots.