You should create full text search indexes for these fields and use MATCH ... AGAINST
This way you can change this line to:
$query = "SELECT * FROM coils MATCH ( name, resistance, wraps, wire_1, wire_2, wire_3, wire_4, wire_5, wire_6) AGAINST ('$term') LIMIT 25";
Updated: If you want stick to string substitution when mounting your
$query (like you did), make sure you have sanitized your
$term variable in order to prevent SQL injection attacks. But it's highly recommended using
bind solution nicely expanded below by @greg-burghardt.
More information about MATCH AGAINST can be found here: https://dev.mysql.com/doc/refman/5.7/en/fulltext-natural-language.html