1. discuss different needs with a view to making a compromise
open/begin negotiations, negotiate a deal/compromise/contract
'To negotiate' means to bargain with another person or party in order to reach an agreement both parties are happy with. Successful negotiating is based on the perceived value of what can be gained and lost by either party. There are many personal and professional situations where you might need to negotiate: for a pay rise; which tasks should be done by who at home; the terms of a contract or agreement, or of a sale. Similar meaning words include 'to haggle', 'to bargain' and 'to come to or reach an amicable agreement.'
2. find a way around or through something
negotiate a way around or through
usually refers to manoeuvring (physically or figuratively) around (or through) an obstacle