How to do setState inside callback: ReactJS

You need to bind correct this (class context) with callback method, then only you will be able to access the class properties and methods.

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Possible Solutions:

1- Use arrow function, like this:

 handleAddNewQuiz(event){
        this.quiz = new Quiz(this.db, this.newQuizName, (err, affected, value) => {
            if(!err){
                this.setState( { quiz : value}); 
            }
        });
        event.preventDefault();
    };

2- Or use .bind(this) with callback method, like this:

handleAddNewQuiz(event){
    this.quiz = new Quiz(this.db, this.newQuizName, function(err, affected, value){
        if(!err){
            this.setState( { quiz : value});  
        }
    }.bind(this));
    event.preventDefault();
};

The way you are using will also work, save the reference of this inside the handleAddNewQuiz method, like this way:

handleAddNewQuiz(event){
    let self = this;    //here save the reference of this
    this.quiz = new Quiz(this.db, this.newQuizName, function(err, affected, value){
        if(!err){
            self.setState( { quiz : value});  
        }
    });
    event.preventDefault();
};

Mayank's answer is correct.. Alternatively you can use https://www.npmjs.com/package/core-decorators

and use the @autobind decorator before the function.