Question 13534
First, I assume that your expression should be:

{{{14x^2 - 17x - 6}}}  Your question did not have the x after the 17.

{{{(2x - 3)(7x + 2)}}} This is the factored form.

How did I get this?  I took the x^2 term (14x^2) and tried (2x)(7x) and then the constant term (-6) and tried (2)(-3) and these worked and I was able to get the correct x-term of -17x.

Check usinf FOIL:

{{{(2x - 3)(7x + 2) = 14x^2 + 4x - 21x - 6}}} = {{{14x^2 - 17x - 6}}}