Steam runs but needs libgl1-mesa-dri:i386, and libgl1-mesa-glx:i386

My answer is more for these issue which is marked as duplicated for this post. I'd installed blank new 14.04.2 64-bit and right then tried to install Steam client (dosn't matter from steampowered site or by apt-get install steam) In result it stucked with

Steam may not run:libGL.so.1

Steam needs to install these additional packages: 
libgl1-mesa-dri:i386, libgl1-mesa-glx:i386
[sudo] password for numb: 
..............................
Reading package lists... Done
Building dependency tree       
Reading state information... Done
Some packages could not be installed. This may mean that you have requested an impossible situation or if you are using the unstable distribution that some required packages have not yet been created or been moved out of Incoming.
The following information may help to resolve the situation:
The following packages have unmet dependencies:
  libgl1-mesa-glx:i386 : Depends: libglapi-mesa:i386 (= 10.1.3-0ubuntu0.4)
  unity-control-center : Depends: libcheese-gtk23 (>= 3.4.0) but it is not going to be installed
                    Depends: libcheese7 (>= 3.0.1) but it is not going to be installed
E: Error, pkgProblemResolver::Resolve generated breaks, this may be caused by held packages. 

Well, I've tried a lot of things. But what had helped (thanks to this answer) was simple - just to install wanted libs with slightly different name:

sudo apt-get install libgl1-mesa-glx-lts-utopic:i386

Your problem is... that you are using a PPA. PPA packages aren't normally multiarch and you need multiarch. To solve this you should remove the PPA:

sudo rename 's/\.list$/.list.disable/' /etc/apt/sources.list.d/*.list
sudo apt-get update
sudo aptitude -f install libgl1-mesa-dri:i386=9.2.1-1ubuntu3 libgl1-mesa-glx:i386=9.2.1-1ubuntu3

That will solve the issue.

I may be late for this but I recently updated my Pop!_OS 19.10 to 20.04 and encountered this issue.
My solution involves downgrading some packages and installing the remaining ones.

Steam installation: you can use any way (I am installing like this)

 sudo apt install steam

The error message:

Reading package lists... Done
Building dependency tree       
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies.
steam:i386 : Depends: libgl1-mesa-dri:i386 (>= 17.3) but it is not going to be installed or
                   libtxc-dxtn0:i386 but it is not installable
          Depends: libgl1-mesa-glx:i386 but it is not going to be installed
          Recommends: mesa-vulkan-drivers:i386 but it is not going to be installed
          Recommends: mesa-vulkan-drivers:i386
E: Unable to correct problems, you have held broken packages.

This worked for me: first fully update all the packages

 sudo apt-get update -y && sudo apt-get upgrade -y

Now, use this to downgrade or install new packages

sudo apt-get install aptitude && sudo aptitude install libgl1-mesa-dri:i386 libgl1-mesa-glx:i386

We use aptitude to ensure that the installation will occur.

Firstly it will ask to keep packages as it is which we don't want so choose "n" press "enter" then choose the next solution "y" followed with an "enter". this will downgrade some packages and install some new packages.

Note: you can choose "?" option for more info.

Again try to install steam.

sudo apt install steam

and you are done. I hope this will help someone. peace.