添加约束,使列仅接受来自另一列的逗号分隔值

我有这两张桌子:

CREATE TABLE `car_shop` (
  `id` int(11) NOT NULL AUTO_INCREMENT,
  `selling_brands` varchar(25) DEFAULT NULL,
  `some_col` varchar(25) DEFAULT NULL,
  PRIMARY KEY (`id`)
) ENGINE=InnoDB DEFAULT CHARSET=utf8

CREATE TABLE `cars` (
  `car_id` int(11) NOT NULL AUTO_INCREMENT,
  `car_make` varchar(25) DEFAULT NULL,
  PRIMARY KEY (`car_id`)
) ENGINE=InnoDB AUTO_INCREMENT=4 DEFAULT CHARSET=utf8

第二个包含以下内容:

+--------+----------+
| car_id | car_make |
+--------+----------+
|      1 | BMW      |
|      2 | Audi     |
|      3 | Toyota   |
+--------+----------+

我需要添加这样一个约束,即selling\u brands列只接受汽车表中填充的值(宝马、奥迪、丰田)。

我是这样想的:

+----+----------------+----------+
| id | selling_brands | some_col |
+----+----------------+----------+
|  1 | BMW, Audi      | shop 1   |
|  2 | Toyota         | shop 2   |
+----+----------------+----------+

我试图添加如下约束,但不起作用:

ALTER TABLE car_shop
ADD FOREIGN KEY (selling_brands) 
REFERENCES cars(car_make)

我得到: 错误:(conn:24)无法添加外键约束 错误代码:1215