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battle (something) out
To struggle against an opponent for something. Those two teams really battled it out in an intense playoff series. My agent and the movie studio are battling out the terms of my contract now.
battle something out
1. Lit. to fight about something to a conclusion. They battled the matter out and came to an agreement. The two young toughs went into the alley to battle out their differences.
2. Fig. to argue something to a conclusion; to struggle to reach a conclusion. The Senate and the House disagree on the bill, so they will have to battle a compromise out.