As the title says it fails to work, it says it requires libcurl3 which cannot be found, libcurl4 exists but no libcurl3...
Same problem on Debian 10 since 2019 (libcurl3 is replaced by libcurl4). I found a working solution:
Download the .deb installer file
In the folder you downloaded the file run:
dpkg-deb -R ./Brackets.Release.1.12.64-bit.deb Brackets
Edit file Brackets/DEBIAN/control and replace libcurl3 with libcurl3 | libcurl4
Rebuild .deb installer running dpkg-deb -b Brackets Brackets-fixed.deb
Install Brackets using the fixed installer running sudo dpkg -i Brackets-fixed.deb
Most helpful comment
Same problem on Debian 10 since 2019 (libcurl3 is replaced by libcurl4). I found a working solution: