1
general::
Phrase(s): go a long way toward doing something [and] go a long way in doing something
Fig. almost to satisfy specific conditions; to be almost right. • This machine goes a long way toward meeting our needs. • Your plan went a long way in helping us with our problem.
McGrawhill's American Idioms And Phrasal Verbs
2
general::
Have considerable effect or influence on. For example, This argument goes a long way toward proving the scientists are wrong, or, as Eudora Welty put it in The Ponder Heart (1954): "It went a long way toward making him touchy about what Uncle Daniel had gone and done." This idiom, then put as go a great way toward, was first recorded in 1697.
American Heritage Idioms