The number of real solutions of the equation $$x(x^2 + 3|x| + 5|x-1| + 6|x-2|) = 0$$ is ______.

$$x(x^2 + 3|x| + 5|x-1| + 6|x-2|) = 0$$.

Either $$x = 0$$ or $$x^2 + 3|x| + 5|x-1| + 6|x-2| = 0$$.

For the second factor: all terms $$x^2, 3|x|, 5|x-1|, 6|x-2|$$ are non-negative. The sum equals zero only if each term is zero simultaneously, which is impossible ($$|x| = 0$$ means $$x = 0$$, but then $$|x-1| = 1 \neq 0$$).

So the only solution is $$x = 0$$. Number of real solutions = 1.

Therefore, the answer is $$\boxed{1}$$.