It sounds to me like what happens when you try to run the 32-bit (i686) version of Firefox on 64-bit Slackware. You can get the 64-bit version at:
http://ftp.mozilla.org/pub/firefox/r...43.0.4.tar.bz2 (This is the US English version, current as of 9 Jan 2016.
Or you can use the directions in
http://ftp.mozilla.org/pub/firefox/r...est/README.txt to get the latest version for any language and any OS.
For what it's worth, I use the binaries from mozilla.org on Slackware 14.1, since the Slackware gang provides the esr version (due to issues with KDE4 -- I use XFCE, so no worries for me).
I just tar the .gz file from Mozilla.org in /usr/local, then link the firefox binary in /usr/bin and edit the desktop file to use the icon in /usr/local/firefox/browser/icons/
I hope that helps!
Stu...