Trial and error is the best way:

The only ordinary way to factor  is as  and 
The only ordinary way to factor  is as  and  
or we will reverse them.

So it must be one of these with the proper signs placed between the terms

(1). 

(2). 

If it's (1), the middle terms must have opposite signs in the boxes
below so that:
              ↏2(a+2b)x ↏ (3a-b)x  =  -(5a-4b)x = -5ax+4bx 

Inspection shows that opposite signs in the two boxes cannot cause the
above to be true.   


So it must be (2), and the middle terms must have opposite signs in the boxes
so that:
              ↏2(3a-b)x ↏ (a+2b)x  =  -(5a-4b)x = -5ax+4bx 

Inspection shows that they must be:
              -2(3a-b)x + (a+2b)x  =  -(5a-4b)x = -5ax+4bx       
 
So in (2) we put - before the (3a-b) and + before the (a+2b):

   

Remove the inner parentheses:

   

Edwin