Are both "in regards to" and "regarding to" correct?

Do in regards to and regarding to imply different meanings or is it okay to use them interchangeably?

Example:

This mail is in regards to your inquiry.
This mail is regarding to your inquiry.

Solution 1:

I would say these are correct:

This mail is in regards to your inquiry.

This mail is regarding your inquiry.

I honestly have never seen this use:

This mail is regarding to your inquiry.

Solution 2:

"In regards to" is a common error, but an error nonetheless. "In regard to" is correct. The "s" would be stuck onto "regard" only if you are saying "as regards," which is a correct alternative.

"With regard to" is also correct.

"Regarding to" is incorrect; "regarding" is all you need to say.