You need to look at the first coefficient and the last coefficient when factoring a trinomial. Please take a look at the attached Word document that illustrates the solution to this problem, thanks!
You can think of it this way (and refer to the attachment):
-on the left side of the X, place the two factors that make up the 1st coefficient -3. It's either going to be 1 and 3 or 3 and 1.
-on the right side of the X, place the two factors that make up the 3rd coefficient -2. It's going to be 2 and -1 or -2 and 1.
-Now is the time to select the correct factors out of the options you have. You do this by cross-multiplying and adding to get the 2nd coefficient, -5. To cross-multiply, take the number on the top-left of the X and multiply by the number on the bottom-right of the X. Also take the number on the top-right number of the X and multiply by the bottom-left of the X. Then add these two numbers. If you use the highlighted factors, you get 1*1 + -2*3 = 1 - 6 = -5. This is how you choose the correct factors.
-For the final step, all you need to do is fill in the factors into the equation (1x-2)*(3x+1). The top left factor and top right factor go into the first set (1x-2) and the bottom left factor and bottom right factor go into the 2nd set (3x+1).