You are misreading the question. It certainly does NOT say "the equation g(x)" because "g(x)" is not an equation. Also you cannot mean that g(x)= 0 is a solution of an equation because the solution of an equation is a number, not another equation.
You mean that is a root of the equation g(x)= 0. Take the third power of each side: and then . Can you differentiate that?