1. **State the problem:** Factor the polynomial equation $$-3x^3 + 27x = 0$$. 2. **Identify common factors:** Both terms have a common factor of $$-3x$$. 3. **Factor out the common factor:** $$-3x^3 + 27x = -3x(x^2 - 9)$$ 4. **Recognize difference of squares:** $$x^2 - 9 = (x - 3)(x + 3)$$ 5. **Write the fully factored form:** $$-3x(x - 3)(x + 3)$$ 6. **Explanation:** Factoring involves finding the greatest common factor first, then applying special factorization formulas like difference of squares to simplify the expression completely.