Answer + factor completely. 2n^2 - 11n + 14 = 3v^2 - 8v - 16 =

I'd like to see some of your own efforts here.  This is the third time you've posted two "factor completelyl" problems, without sharing what you've already done.

3v^2 - 8v - 16 cannot be reduced.  Thus, your best choice to find roots is to apply the quadratic formula:

         8 plus or minus sqrt( 64-4(3)(-16) )
v =
                                2(3)
        8 plus or minus sqrt( 64 + 192 ) 
   =
                                 6
         8 plus or minus sqrt(256)
    =
                             6

     = 8 + 16, all divided by 6, or    8 - 16, all divided by 6

     = 4 or -8/6, or 4 or -4/3.

The factors are (v-4) and (v + 4/3).