How to factoring quadratics by grouping 2x^2-5x+3

There aren't enough terms to factor this by grouping; you need at least four, at least as far as i know? trinomials are usually pretty easily factored by trial and error

(2x - 3) (x - 1)

is how it factors down. you know that two only has two factors (2 and 1), so you always have (2x + _) and (1x + _) for trinomials beginning with 2x^2. from there, i usually just plug in factors of your constant (3, in this case) and see which ones fit the empty spaces!