Solution 1:

This comes down to a matter of opinion, but as a long-time editor I prefer the hyphenated version because it is easier for me to read. Collins, Cambridge and Macmillan agree with us, while Merriam-Webster, Wikipedia and the Business Dictionary (among others) show it as unhyphenated. Consider your audience and choose what works best for you. Younger readers may be more likely to be comfortable with reengineering, while older folks (like me) may find it a bit odd if it lacks the hyphen.