To install Synaptic
sudo apt install synaptic
Then you can open Synaptic from your app menu. You will be prompted for a password since Synaptic must access Root. Once open, look at the Vertical Left Pane- toward the bottom are buttons;
Sections
Status
Origin...
Click on Custom Filters. On the Upper portion of the Side Pane, you will see
All
Broken...
Click on Broken.
If you have broken packages, you will see them listed- Right Click on the package to select your option.
Otherwise:
Open Synaptic, then click the Search Button on the Top Toolbar. Type in mysql.
It will list your mysql packages and show whether they are Installed, Broken, etc. You can right click for options such as "Remove Completely."
You must then hit the Apply button on the top toolbar.
If able to remove them, you can search again for mysql and then select the mysql packages with a right Click and choose install.
You must then hit the Apply button on the top toolbar.
The Package list on Synaptic can be confusing when you first start using it. I remember the first time I used Synaptic, I was so bewildered, I almost never used it again. But it is easy to learn- feel free to post screenshots of what packages are listed if you would like to confirm your steps as you go.