The long synopsis is a collaborative effort between you and your agent. There was a time when this was called a chapter-by-chapter outline and some publishers still ask for that. Most publishers, however, have moved on to the narrative synopsis, or long synopsis.
It begins just like the short synopsis and should cover all the same points, but now you have three double-spaced pages in which to tell your story.
With all that extra space you can hint at other plot complications and characters that add flavor to a story. But remember to make it read like a short story in three pages.
This is most often the "decision document," the one thing on which yes or no decisions are generally made. If the editor needs to get an OK from a supervisor or a committee, this will be the document that is used for the presentation.
Review the pages for loglines, web synopsis and short synopsis. Take a look at your logline, web synopsis and short synopsis. Now, write what you wanted to write in the first place, just remember your audience and keep it to three double-spaced pages.