Question

How do you factor `4v^2-9v-9`?

Answer 1

`4v^2-9v-9`

`=(4v-3)(v+3)`

But how to get there is a little more complex.

Start by looking at factor pairs of `4`
(that is values `(a,b)` such that `axxb=4`)
and
factor pairs of `9`
(again, values `(p,q)` such that `pxxq=9`)

There are only a very few possibilities
`4 = (4xx1)` or `(2xx2)` or negative versions of these pairs
`-9 = (9xx-1)` or `(3,-3)` or negative versions of these pairs

We are looking for values `(a,b)` and `(p,q)`
such that
`(av+p)(bv+q) = 4v^2 -9v -9`

Because of our restrictions on possible factor pair values
we simply need to find the two pair factors that give
`aq+bp = -9`

Since there are not a lot of combinations
the two pairs `(4,1)` and `(-3,3)` soon become obvious.