Use get_post_types to query only custom posts types

I need to query only custom posts types – that is all post types in my WP install excluding posts and pages. I have used get_post_types to build a string of all custom post types which I want to query:

$args=array(
    'public'                => true,
    'exclude_from_search'   => false,
    '_builtin'              => false
); 
$output = 'names'; // names or objects, note names is the default
$operator = 'and'; // 'and' or 'or'
$post_types=get_post_types($args,$output,$operator); 

// Loop thru the cpts and assign a related taxonomy to a variable
$posttypes_array = "";
foreach ($post_types  as $post_type ) {
    $posttypes_array .= "$post_type, ";
}
$posttypes_array = rtrim($posttypes_array, ', ');
echo $posttypes_array;

The output for the variable $posttypes_array is this string:

'puzzles', 'quizzes', 'challenges', 'tales', 'can_you_help'

My issue is that I can’t use this variable to query all of these post types like this:

$buildArgsAllQuestions = array( // Add out new query parameters
    'post_type' => array($posttypes_array),
    //'post_type' => $posttypes_array,
    'orderby' => 'date',
    'order' => 'DESC',
);

My query for all custom posts only works when I use this line for post_type:

'post_type' => array( 'puzzles', 'quizzes', 'challenges', 'tales', 'can_you_help' ),

Can anyone tell me how I can use the variable $posttypes_array or something similar to query all custom posttype like this: 'post_type' => array($posttypes_array) ?