Xr = the position of the joystick in the game
Xt = the change in position because of the trimming
Xg = position of the joystick of the gamer. In case of the X65F Xg = Fg
Fg = force applied to stick by the gamer
Fr = force the a real person would need to apply
Important to know here: Xr directly affects the position of the ailerons. (In most planes)
When the ailerons are in a neutral position the aircraft does not always flight straight because of speed, load balance, ... . In order to maintain a level flight the pilot needs to reposition his stick to a position Xr. Nature does not like this and will try to push the ailerons back to its neutral position. The pilot experiences this by the force Fr on the stick. The player must do the same, he must reposition his stick to Xg and this requires, on most sticks, a force Fr because of the centering (or FFB).
Nor the player nor the real pilot likes to keep applieing force. The pilot would now trim his aircraft so the pressure will be relieved. However his joystick does not change its position. With FFB you would have the same experience. Xr = Xg
With non-FFB sticks you can't do that. So usually they will relieve the player from the force by change the mapping between the players and the real pilots with the following (or similar) formula: Xr = Xg + Xt. This means that when the play released his joystick after trimming, the plane will flight straight even thought the real pilot's stick (and thus the ailerons) would not be centred. But both the real and virtual pilot can release there stick and still flight straight. This also implies that when the gamer pulls fully back on his stick, the real pilot's stick would not be fully back if there was trimmed forwards.
Remarks:
FFB sticks in a game not supporting FFB probably behaves like non-FFB sticks.
y = x should be interpreted as y = f * x where f is a factor or is some cases another function.
Disclaimer: this does not applies to all planes and I am no expert on this matter.