I will assume that you meant 6x^2 - 7x - 3.
So you factor this out as follows:
List all factors of 6 and 3:
6: 1 and 6, 2 and 3
-3: 1 and -3, -1 and 3
Now which pair of factors in both 6's factor group and of 3's factor group will combine together to give you -7?
Like this:
3 x -3 = -9 (here i take factors 2 & 3 from 6 and 1 & -3
2 x 1 = 2 from 3 and I find a combination so that the
so -9 + 2 = -7 sum or difference of the products produce
-7)
Now we can do the factoring:
(3x + 1)(2x - 3)
To prove that this is the correct factored form check it:
3x * 2x = 6x^2
---------------------------------
3x * -3 = -9x
1 * 2x = 2x so -9x + 2x = -7x
---------------------------------
1 * -3 = -3
so you're back to the equation 6x^2 - 7x - 3