I have a similar problem as the one presented in the question No Entity Framework provider found for the ADO.NET provider with invariant name 'System.Data.SqlClient'
I got this error but for me it was something entirely different.
I had to edit:
C:\Windows\Microsoft.NET\Framework64\v4.0.30319\Config\machine.config
And:
C:\Windows\Microsoft.NET\Framework\v4.0.30319\Config\machine.config
Searching for DbProviderFactories both configs looked like this:
When I removed the trailing everything started working again.
I was able to solve it by looking at only Unable to find the requested .Net Framework Data Provider and finding this answer:
https://stackoverflow.com/a/9929534/3850405