Question 422980
Answer: First we factor the expression, after equalize it with zero:

   {{{ 3x^3+3x=3x*(x^2+1)}}}

 The product {{{ 3x*(x^2+1)=0 }}}, when 3x=0 or x=0

 The factor {{{x^2+1 }}} is always positive for every value of x.

 The only root for our equation is {0}.