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These web parts use the SQL search engine. You can also try index-based searching provided by the Smart search module. Smart search offers better performance than SQL search but requires more configuration steps.
If you want to let users search forum posts for some given text, you can use the Forum search box and Forum search results web parts. You will typically place them both on the same page. However, if you need to place the forum search box on a different page, you can set its Redirect to URL property to the page where you have the Forum search results web part, such as ~/SearchForum.aspx.
You can also use the Forum search - advanced dialog web part, which offers a larger dialog that allows users to specify multiple search parameters.
If you wish to use the basic search box by default, but want to let users have the option of using the advanced dialog as well, you can do so by entering the path to the page containing the Forum search - advanced dialog web part into the Advanced search path property of the Forum search box web part. This will display an Advanced search link next to the search box.