If the solution is an invasion, then it will fail because locals know their country, know how to trick the invader (especially if there isn't a soldier per inhabitant).
Soldiers cause collateral damages, making it even more easy for the insurgents to hire people ready to hurt troops.
Besides, terrorists are not sent by governments, so there is no point in invading a sovereign country without absolute proof of their involvement.
There are countless existing levels where terrorists can be prevented from acting: ID cards, surveillance cameras, police patrols, checking passengers at ports and airports where they embark for the US. No terrorist can act alone and be effective. He'll need to contact a network and only one mistake is enough for the police to uncover an entire network. Neighbours can also be of help. In order to be effective, terrorists need time , and time can also be an effective weapon against them (because you need to gather evidence).
No, invading a country with an army is an act of war and a demonstration of an imperialistic behavior...It can't succeed., also because it brings huge stresses to the invaded (who are motivated to defend what they are) but also to the soldiers (who are in a foreign country, incapable of communcating and trusting the locals).