Hi!
I think the easiest method here is using a calculator, but obviously you want all the steps so I'll just go through them quickly.
We know that to get to 3x^2 we need 3x and x together so now we already have half of our factorisation done -- (3x + n) (x+p)
Now we need to find n and p
For the -22x we can get through our previous knowledge, which is the fact that there is a 3x somewhere in there, AND another x in there as well, so we can just do 3 * -7 which equals -21 and then for the other x we can do it x * -1 which is -x -- just add those together and they equal -22x.
Usually for the second thing (usually with x) in the equation its always addition of the two different variations (not sure if i'm explaining this right)
After it, the third thing in the equation is ALWAYS multiplication, so since we already have -1 and -7 we can easily just multiply those together and get +7
What the main thing to realise here is that the two variations that you have found fit into BOTH the addition and the multiplication processes, so even if you found something in the first addition thing that added up to -22 but didnt multiply together to make +7, then it's WRONG! My method is probably really wrong but it's the only way I can really do it, I'm sorry if it isn't that helpful lol
which overall gives us the information we need;
(3x-1) (x-7) is the answer -- in case ur confused which one is n and which one is p, just remember that 3x HAS to be multiplied by -7 so it cannot be in the same bracket.
I'm really sorry if this explanation was all over the place lol.