go a long way toward doing
go a long way toward doing somethingand 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.
go a long way toward
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.