Searching A Database Using The Name Of Person

I want to search my database using a person's name. My names are separated into 'First' and 'Last' name fields.

The SQL I'm using so far works if you search only by the first name, or only by the surname, but if you enter both names, it comes back with no results.

How do you do it so that it will work in all cases?

Here's my code:

Sql = "SELECT * FROM kbs, authors WHERE authors.authorID = kbs.author"

If Request.Form("TypeSearch") = "author" Then
Sql = Sql & " AND (authors.authorLastName LIKE '%" & Request.Form("kbsSearch") & "%' OR authors.authorFirstName LIKE '%" & Request.Form("kbsSearch") & "%')"
End If

set rs = Server.CreateObject("ADODB.Recordset")
set rs=conn.execute(Sql)