Factor 2x2 + 14x - 3x - 21 by grouping.
The first two terms have 2x in common, which we can factor out to find
2x(x + 7) - 3x - 21.
For the second two terms, we could factor out 3 or we could factor out - 3. Whoa! Rein in your pony there, cowboy. If we factor out 3, we'll find
2x(x + 7) + 3(-x - 7).
Those two terms don't have a common factor. Instead, if we had factored out - 3 we would get
2x(x + 7) - 3(x + 7)
and we could pull out (x + 7) to see that
(2x - 3)(x + 7).