Hi thesip2323,
To start, most GMAT questions can be approached in more than one way - and it's worth noting that you do NOT need to approach this question Algebraically to solve it (and by extension, if you are choosing methods that involve more complicated math than is necessary, then you might just be making everything harder than it needs to be).
That all having been said, when dealing with a Quadratic in which the first term includes a co-efficient that is greater than 1, a bit of 'brute force' Arithmetic is usually required to factor the Quadratic. Thankfully, there are usually context clues for what the possible values will be (and there won't be that many). Here, the clues are:
1) The "-35" at the end of the equation; this will be the PRODUCT of the two numbers, so we know that one number will be negative and one will be positive. Second, there are only a couple of ways (that involve integers) to get to 35: 1 x 35 and 5 x 7.
2) Similarly, the "6X^2" at the beginning is likely just one of two options: (X)(6X) or (2X)(3X).
3) The "-23X" in the middle will be the result of adding a positive and a negative (remember that "-35" at the end: the product of one positive and one negative, so the two terms that sum to make that middle term will be one positive and one negative). Since that term is not bigger than 35 (and not that close to 35 either), it's likely that we're NOT going to be dealing with 1 x 35 (it'll probably be a 5 x 7).
Now it's just a matter of doing the 'brute force' work. How long will it take to multiply and add the various possible calculations to get to "-23X"? It's important to do all of that work on your pad, since even if one of your calculations doesn't hit that total, you might spot a pattern that will help you to find the actual terms that will.
GMAT assassins aren't born, they're made,
Rich
Contact Rich at: Rich.C@empowergmat.com