Use double quotes instead of single quote eg :
where('customer.name', 'LIKE', "%$findcustomer%")
Below is my code:
public function searchCustomer($findcustomer)
{
$customer = DB::table('customer')
->where('customer.name', 'LIKE', "%$findcustomer%")
->orWhere('customer.phone', 'LIKE', "%$findcustomer%")
->get();
return View::make("your view here");
}