The goal of US in the Vietnam War was to prevent the Communist North Vietnamese, backed by the USSR and the PRC, from bring down the government of South Vietnam.
The U.S. failed because many Vietnamese in South Vietnam resented the existence of a foreign force in their country. They would rather have their government fall than succeed due to foreign involvement. Further, the North Vietnamese were particularly persistent, absolutely refusing to give up, and not even a nuclear attack was going to be able to defeat them. Thirdly, many troops (U.S. troops) had morale problems due to questioning the validation of the war and the knowledge that the Vietnamese had apparently never heard of the Geneva Convention concerning dealing of captured enemy soldiers, plus the reality that an approaching child might be a suicide bomber which creates a further moral dilemma. Shoot a child or possibly not shoot, and the child blow up and so do you.