Google Calendar - Find a Time Feature
Google Calendar has a Find a Time feature you can use to help you find a common time that works for everyone you have invited - you can even prioritize to only some of the invitee's calendars to ensure that those crucial for the event are there.
A small word of caution - this only works well if everyone is using Google Calendar as their planner and keeping it up to date :-)
Here is a video on how to find a time, if you prefer.
To use this feature, click on the More options button when creating the event -
Over on the right side of the event information window, add the guests you want to include in this event -
On the right side, next to the words Event Details is the Find a Time option - click on that -
It defaults by showing a Week view, so you can see everyone's open time over that whole week -
You can also view it in a Day view which will show everyone's free/busy time in a side-by-side look -
Finally, if there are some people that MUST be in attendance, but others that are optional, you can uncheck boxes next to names. It will appear without that information, making your decision a bit easier (hopefully).