Laravel 6.x : Update method in UserController

Hello everyone I allow myself to come to you because I am faced with a problem indeed when I want to implement the update method in my user controller it does not work I explain two. When I go to my edition view of wrestling games, my data is good but when I modify it and send it nothing happens I just come back to a page with a message telling me that my data is up to date in my table no update data I join my controller saw me and my routes

Controller :

public function update(Request $request, User $user) { // $user = User::findOrFail($id);

$request->validate([
    'firstname' => 'required',
    'name' => 'required',
    'email' => 'required',
    'usertype' => 'required',
]);

$user->update($request->all());

return redirect('/role-register')->with('status', 'The account is update !');

}

Edit view :

<div class="container">
        <div class="row">
            <div class="col-md-12">

                <div class="card">
                    <div class="card-header">
                        <h4>Edit register roles</h4>
                    </div>
                    <div class="card-body">

                            <form action="" enctype="multipart/form-data" method="POST">
                                @csrf
                            @method('PUT')
                                <div class="form-group">
                                    <label>First Name</label>
                                    <input type="text" name="firstname" value="" class="form-control">
                                </div>

                                <div class="form-group">
                                    <label>Name</label>
                                    <input type="text" name="name" value="" class="form-control">
                                </div>

                                <div class="form-group">
                                    <label>Email</label>
                                    <input type="email" name="email" value="" class="form-control">
                                </div>

                                <div class="form-group">
                                    <label>Give role</label>
                                    <select name="usertype" class="form-control" value="">
                                        <option value="admin">Admin</option>
                                        <option value="user">user</option>
                                    </select>
                                    <button type="submit" class="btn btn-success">Update</button>
                                    <a href="" class="btn btn-danger">Cancel</a>
                                </div>
                            </form>

                    </div>
                </div>

            </div>
        </div>
    </div>

Route :

Route::group(['middleware' => ['auth', 'admin']], function () {

Route::get('/dashboard', function () {
    return view('admin.dashboard');
})->name('dashboard');

Route::get('/role-register', 'Admin\DashboardController@registered')->name('role.register');

Route::get('/role-edit/{id}', 'Admin\DashboardController@edit')->name('role.edit');

Route::put('/role-register-update/{id}', 'Admin\DashboardController@update')->name('role.update');

Route::delete('/role-delete/{id}', 'Admin\DashboardController@destroy')->name('role.delete');

Route::get('/cutomers', function () {
    return view('admin.customer');
})->name('customers.list');

});

Thx for helping me

via Chebli Mohamed