To understand why there are no solutions, you have to understand what Bush and the Republicans did to Iraq to put that country in such a terrible position.
Of course, the invasion was the first problem. Iraq never attacked the United States. They didn't ask to be "freed". The saw us from the first as invaders, not liberators.
The most obvious is that Republicans and Bush had no idea there was a difference between Sunni and Shiite. All they saw were "Muslims". By not knowing the religions or the people, there was no understanding of what "not to do". So Republicans blundered into doing everything wrong they could possibly imagine.
Iraq had an active duty military of 250,000 and an inactive reserve of 500,000 making it one of the largest armies in the world. Bush and the Republicans fired them. Just let 250,000 armed and trained men go. Suddenly they had no jobs and no money for their families. But they still had their weapons and a new found hatred of the US.
If Bush and the GOP knew anything about the Iraqis, they never would have put Shiites into power thereby creating a sister state with Iran.
Republicans helped those Shiites author a right wing, extreme Islamic Constitution:
Article 2:
First: Islam is the official religion of the State and it is a fundamental source of legislation:
A. No law that contradicts the established provisions of Islam may be established.
Full Text of Iraqi Constitution