Verified answer

Apply the quadratic formula.

This gives us (22 ± 24) / 6, or roots of -1/3 and +23/3

3 (x+1/3)(x-23/3)

This does not factor over the integers, but it does factor over the rationals.

(3x+2)(x-8)

You just plug in numbers and check. At least that's how I find them. I know that 3x*x is 3x^2. Then you have to look for a number that you can multiply 3 by to give you -24..which is -8.