If you're trying to activate a serial key and getting the error 'The serial number (xxx) is not valid for this product', the most likely cause is that you're using the Product ID and not the serial key.

Serial keys look like this: 123-456-123456-1234.

With user account licensing you don't need your serial key to activate your license, you can activate by logging in with your Redgate ID and this ensures that you never run out of activations. On the toolbar of the tool, click on Help > Manage license. 

If you're activating on a machine without an internet connection you will need your serial key. To view your serial key click on Licenses > select the tool > Serial Number tab.