Date saves to database as 0000-00-00 00:00:00

Hello there, I hope someone can help. Ive been researching for sometime now on how to properly save from a form to the database when a user choose a specific date. On the create page it looks as such:

create.blade.php

{!! Form::label('published_date', 'Published Date', ['class' => 'control-label']) !!}
                            {!! Form::input('date', 'published_date', date('Y-m-d'), ['class' => 'form-control']) !!}

Controller (Store)

    {
        $binding        =       Binding::with('id');
        $categories     =       Categories::with('id');
        $conditions     =       Condition::with('id');
        $editions       =       Edition::with('id');
        $publishers     =       Publisher::with('id');
        $rarities       =       Rarity::with('id');
        $signatures     =       Signature::with('id');

        // Availability option switch (on = 1; off = 0)
        $available  =   Input::all();

        // Convert added_date format to be compatible with database ISO 8601 format
        $added = Input::all();
        $added['added_date'] = date('Y-m-d', strtotime($added['added_date']));

        // Convert published_date format to be compatible with database ISO 8601 format
        $published = Input::all();
        $published['published_date'] = date('Y-m-d', strtotime($published['published_date']));

        $book = new Book($request->all());
        Auth::user()->books()->
            save(
            $book,
            $binding,
            $categories,
            $conditions,
            $editions,
            $publishers,
            $rarities,
            $signatures,
            $added,
            $published,
            $available);


        return redirect('admin/library');

Controller (Show)

    public function show($id)
    {
        $books = DB::table('books')->where('books.id', '=', $id)
                ->join('bindings', 'books.binding_id', '=', 'bindings.id')
                ->join('categories', 'books.category_id', '=', 'categories.id')
                ->join('conditions', 'books.condition_id', '=', 'conditions.id')
                ->join('editions', 'books.edition_id', '=', 'editions.id')
                ->join('publishers', 'books.publisher_id', '=', 'publishers.id')
                ->join('rarities', 'books.rarity_id', '=', 'rarities.id')
                ->join('signatures', 'books.signature_id', '=', 'signatures.id')
                ->join('users', 'books.user_id', '=', 'users.id')
                ->first();
        
        return view('admin.library.show')
            ->with('books', $books);
    }

Model

use Carbon\Carbon;
use Illuminate\Database\Eloquent\Model;

class Book extends Model {

    /**
     * @var string
     */
    protected $primaryKey = 'id';

    /**
     * Allowed Fields for mass Input
     *
     * @var array
     */
    protected $fillable = [

        'title',
        'author',
        'sec_author',
        'thi_author',
        'for_author',
        'availability',
        'barcode',
        'isbn',
        'dewey',
        'universal',
        'loc',
        'added_date',
        'binding_id',
        'category_id',
        'condition_id',
        'edition_id',
        'publisher_id',
        'rarity_id',
        'signature_id'

    ];

    /**
     * @var array
     */
    protected $dates = ['added_date', 'published_date'];

    /**
     * @return array
     */
    public function getDates()
    {
        // Return any columns that are date or datetime types
        // to automatically have Laravel convert them to Carbon
        // objects. (Also include created_at, updated_at and
        // deleted_at if you use them)
        return ['added_date', 'published_date'];
    }

    /**
     * @param $date
     */
    public function setAddedDateAttribute($date){

        $this->attributes['added_date'] = Carbon::createFromFormat('Y-m-d', $date);
    }

    /**
     * @param $date
     */
    public function setPublishedDateAttribute($date){

        $this->attributes['published_date'] = Carbon::toFormattedDateString('Y-m-d', $date);
    }

I have tried a bunch of different methods from what I have read and saw, but honestly I cant believe it can be this complex for a user to simply choose from a datetime picker in the form and save it. My frustration level is high :( A big thank you to everyone in advance.