"endeavored to explain" is correct and usable in written English.
You can use it to indicate that someone attempted to provide an explanation about something. For example, "The teacher endeavored to explain the complicated algebraic concept to the students."
Most nervous person in the audience, and in an interval between periods of fidgeting endeavored to explain symptoms of how he felt.
In the course of forty years, and more than a dozen books, Dennett has endeavored to explain how a soulless world could have given rise to a soulful one.
He has explained the payments from businesses as consulting fees, although some were earned while he was holding public office, and he has endeavored to explain the bank transfers as well.
Robert Giroux sent a copy of "Wise Blood" to Evelyn Waugh hoping for a blurb, and Waugh replied, "The best I can say is: 'If this really is the unaided work of a young lady, it is a remarkable product.' " One should pretty much ignore her own pronouncements on her art, though in her last years she increasingly endeavored to explain her intentions.
Matters quickly went down the Rabbit Hole when Mr. Stein endeavored to explain the "personal reasons" behind his sudden withdrawal.
As the plane strained against the buffeting, prompting a mixture of whimpering and self-denying hilarity from the passengers, my friend spun round in his seat and, seeing me near-hysterical, endeavored to explain the mechanics and the back-up systems the meticulously engineered unlikelihood that it could all go wrong.
I could endeavor to explain what his story has to do with either Profane's picaresque adventures or Stencil's search for V.
WASHINGTON — American Airlines and the Federal Aviation Administration, endeavoring to explain the biggest disruption to air travel in years, disagreed on the fundamental facts in reports each submitted to the federal transportation secretary.
JASPER, Ind .— At a candidate forum here last week, Representative Baron P. Hill, a threatened Democratic incumbent in a largely conservative southern Indiana district, was endeavoring to explain his unpopular vote for the House cap-and-trade energy bill.
We endeavor to explain the flexibility inherent to the twisted method, through examples and new computations, in order to suggest further applications.
Such a program would endeavor to explain why it might remain acceptable for self-aware error theorists to retain their realist-seeming moral discourse.
