Explain how to completely factor this : )

4(2x^2 + 17x + 21) This reduces the size of the numbers you need to try.
It's going to look like this when you factor
4(2x + ___) (x + ___)
Now its a guessing game.  Start with 7
4(2x + 7)(x + 3) you need the 3 to multiply to 21
But the middle term when you expand this is 7x + 6x = 13x which does not work. Try switching the 7 and 3.

4(2x + 3)(x + 7)
This your answer. because 3x + 14x = 17x.