When you go for mixed mode then you need to use SqlServerAdmin (sa)authentication and as the policy of the SQL you can not keep sa password as empty, see below steps to change the authentication mode
To change security authentication mode
1.In SQL Server Management Studio Object Explorer, right-click the server, and then click Properties.
2.On the Security page, under Server authentication, select the new server authentication mode, and then click OK.
3.In the SQL Server Management Studio dialog box, click OK to acknowledge the requirement to restart SQL Server.
4.In Object Explorer, right-click your server, and then click Restart. If SQL Server Agent is running, it must also be restarted.
To enable the sa login
1.In Object Explorer, expand Security, expand Logins, right-click sa, and then click Properties.
2.On the General page, you might have to create and confirm a password for the login.
3.On the Status page, in the Login section, click Enabled, and then click OK.
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Microsoft MVP 2014 [ASP.NET/IIS]