How to add custom taxonomy to search

So I have custom taxonomy called “cars”. I would want that when user does search, it would also search through taxonomy. Meaning that in “cars” taxonomy if I have “Audi” term and user search with keyword “audi” it would then return posts that are tagged with term “audi”.

I tried this:

function mytheme_pre_get_posts( $query ) {
$query->set( 'tax_query', array(
        array(
            'taxonomy' => 'cars',
            'field'    => 'name',
            'terms'    =>  $_GET['s'],
        )
    ));
add_action( 'pre_get_posts', 'mytheme_pre_get_posts', 1 );

But that breaks the search completely. Can this be done even or did I miss something?

You could try unsetting the original search query, otherwise you may be doubling up and the combination results in nothing? eg, try adding to your function:

$query->set('s','');

UPDATE

I am not sure on this one, but you could try the AND operator -I think this adds to the existing query instead of replacing it…

function mytheme_pre_get_posts( $query ) {
    if ( !is_admin() && $query->is_search() && $query->is_main_query() ) {
        $term = get_term_by('name', get_query_var('s'), 'cars');
        if ($term) {
            $query->set( 'tax_query', array(
                 array(
                    'taxonomy' => 'cars',
                    'field'    => 'slug',
                    'terms'    =>  $term->slug,
                    'operator' => 'AND'
                )
            ));
         }
    }
}
add_action( 'pre_get_posts', 'mytheme_pre_get_posts', 1 );

Note: changed use of field name as mentioned by @PieterGoosen to slug, and pre-fetched term slug to pass to tax query, and extra conditions as mentioned by @birgire.