You might first try to make a 40/20 fan dipole. Basically it's two dipole antennas in one. The top wire will be a standard 40 meter dipole and below that (but attached together at the center) will be a 20 meter dipole. Some tuning will be required since one dipole will affect the other but once you have the tuning right no further adjustments should be required. You'll actually end up with a 40/20/15 meter dipole since the 40 meter dipole will also work on 15 (but SWR will be a bit high although generally it's close enough). Be sure to keep the two dipoles separate except at the feed point. You can either fan them out or make insulated spacers (6" or longer recommended).
Often having the two connected will shorten the lengths by a bit, but initially cut them for the full length and adjust from there (it's easy to shorten but hard to lengthen the wires). It's best to tune the higher frequency bands first and then the lower bands, but you'll end up adjusting both either way. It's best to not cut the wire until you have both bands tuned. Simply twist the extra wire back on the existing wire until everything is tuned properly. An antenna analyzer makes this process much easier.
Note, if you want to improve your 15 meter performance, do a search on how to best do this. Many folks recommend a "bow tie" wire attached to the standard 40 meter dipole about 11 feet from the center (on both sides). This should also be tuned so don't solder it in place until you have the tuning correct and check the other two bands to make sure that they are still properly tuned and adjust as necessary. Adding this while the wire is new and still shiny will make soldering it in place much easier.
Some folks just attach the two dipoles at the same point in the center while others make a longer connection point to help isolate the fan elements. I know folks that swear by both so just pick which ever works for you. There are many designs and instructions on the web so I won't give you specifics here. My 40/20 fan dipole has great SWR on both 40 and 20 and with my built-in autotuner I can work all bands from 40 through 6. If I had the space, I'd add an 80 meter fan and hopefully could cover all bands but 160. My version is probably HOA friendly since it's mounted on the side of my fence. If I mounted it higher I'd probably have better results but in under 2 years I've gotten WAS on several bands and my DXCC so it must be doing something right.