Keith McMillan explains what the creative play-caller will bring to Washington. (Jayne Orenstein/The Washington Post)

The Washington Redskins got it right Thursday in hiring Jay Gruden as their next head coach. Owner Daniel Snyder and General Manager Bruce Allen needed fewer than two weeks to complete a process some in the organization privately hoped would end with Gruden, formerly the Cincinnati Bengals’ offensive coordinator, becoming the team’s eighth coach since Snyder purchased the team in 1999. Now comes the hard part for Gruden: fixing Robert Griffin III.

Although the Redskins have many problems, none is bigger — and potentially more damaging to the franchise long-term — than the one at quarterback. Gruden must be given time to rebuild a roster in disrepair and establish his style in an effort to turn around a team that has finished last in the NFC East five of the past six seasons. But the longtime NFL assistant has to work quickly in both helping Griffin improve on the field as a pocket passer and restore the quarterback’s tarnished image off of it. The latter could prove to be more difficult.

As part of his get-fired-and-get-paid strategy, former Redskins coach Mike Shanahan revealed that Griffin’s chummy relationship with Snyder undermined the team’s dynamic. Gruden’s predecessor succeeded in casting Griffin as an out-of-control spoiled brat. Anyone who read my friend and colleague Sally Jenkins’s recent column on Griffin knows what I mean. Jenkins was too harsh on Griffin, but he does have some fence-mending to do at Redskins Park.

When Gruden speaks with players about Griffin, many will tell him they’re still united behind the 2012 NFL offensive rookie of the year. They’ll say they’re confident Griffin is the best person to lead them under a new coaching staff. The Redskins will leave no doubt Griffin still is respected in the locker room.

Some veterans, however, undoubtedly will suggest Griffin should take more responsibility when things go wrong. It wouldn’t be surprising if Redskins offensive linemen reveal Griffin was too quick to point in their direction during an embarrassing 3-13 season. For an organization torn apart by infighting in the previous regime, Gruden will discover, the healing process can be accelerated if Griffin gets back on a good path.

Before Gruden starts working on X’s and O’s, he’ll have to earn Griffin’s trust. To his detriment, Griffin blocked out Shanahan and his son Kyle, the offensive coordinator, who Griffin thought were in cahoots against him. Third-string quarterback Rex Grossman had a spot on the roster, people within the organization said, because the warring factions needed an intermediary.

The Shanahans devised a spectacularly successful offense that topped the league a season ago and helped Griffin have a groundbreaking year for a rookie signal-caller. Griffin, though, felt threatened by the Redskins’ father-son coaching tandem. No matter the situation, Griffin believed the Shanahans were aligned because of what they shared: blood.

Gruden’s brother, Jon, is a Super Bowl-winning coach, and the Redskins could use as many sharp football people as possible to help clean up this mess. After what happened with the Shanahans, however, Snyder probably is done with family acts for a while. Griffin is eager, people familiar with his thinking say, to build a bond with a coach whose only agenda is to help the Redskins thrive.

Considering Griffin’s poor play and missteps — he and his father erred in pushing for major changes in the offense publicly — some Redskins fans are ready for turnover at quarterback, too. Many believe the organization should stop catering to Griffin. Those people also suffer from short memories.

The Redskins gave up four high-round draft picks for the opportunity to select Griffin. In completing the deal, the Redskins will send their first-round pick in the upcoming draft — No. 2 overall — to the St. Louis Rams. The Redskins mortgaged their future for Griffin.

Although team management has done some crazy things through the years (like guaranteeing Albert Haynesworth $41 million), turning away from Griffin now would set a new franchise low. The Redskins knew they had to bring in someone who could help them maximize the return on their investment in Griffin, and Gruden clearly has the credentials.

Under Gruden, Bengals quarterback Andy Dalton emerged as a solid quarterback capable of guiding a team to the playoffs. Dalton hasn’t had postseason success, but Redskins fans should ask themselves this: Wouldn’t you be happy if Griffin rebounds enough to lead the team to consecutive playoff appearances?

Griffin needs much work as a pocket passer — “Right now, he’s a project,” a longtime member of the franchise told me recently — so the Redskins’ help-wanted ad might as well have read: “Quarterback doctor needed.” When word emerged Wednesday the Redskins were close to finalizing a deal with Gruden, a team official told me Gruden would be the perfect fit for Griffin because, foremost, Gruden’s an outstanding teacher.

There are no guarantees Griffin will ever become an elite pocket passer. And Griffin may never again be as popular with fans as he was during his magical rookie season. But in choosing their next coach, the Redskins put Griffin first — and that’s exactly what they needed to do.