Question 8426
Factor:

{{{16b^2+10b-21 = (8b-7)(2b+3)}}} 

How did I arrive at this solution?  Trial & error mostly.

 I know that I needed the factors of -21.
 Well, there aren't that many so I tried:
 (-1)(21), (1)(-21), (-3)(7), and (3)(-7)

I also know that I needed the factors of {{{16b^2}}}.

I tried: (16b)(b), (2b)(8b), and (4b)(4b)

So I tried these in various combinations to give the desired middle term of +10b.  It didn't take too many tries to get:

{{{(8b-7)(2b+3)}}} as the factors of {{{16b^2+10b-21}}}