This trinomial can be factored as two binomials.
So setup two sets of parenthses.
8x² can be factored as 8x · x or 4x · 2x
and -3 can be factored as +3 · -1, -1· +3, -3 · +1, or +1 ·-3.
If the middle term in the original trinomial is even,
try pairs of even factors first if you have that option.
In this case, we have a 4x and a 2x so let's try those first.
Let's do this with all the factors of -3.
So our first possible answer could be (4x + 3)(2x - 1).
Since the product of the outer terms, -4x, plus the product of the inner, 6x,
doesn't add to our middle term, this pair doesn't work.
Now let's try (4x - 1)(2x + 3).
The product of the outer terms, 12x, plus the product of the inner, -2x,
equals the middle term in our original trinomial, this pair works.
So our answer is (4x - 1)(2x + 3).