1. **State the problem:** Simplify and solve the expression $3x(3x+3)$. 2. **Use the distributive property:** Multiply $3x$ by each term inside the parentheses: $$3x \times 3x + 3x \times 3$$ 3. **Calculate each product:** $$3x \times 3x = 9x^2$$ $$3x \times 3 = 9x$$ 4. **Combine the results:** $$9x^2 + 9x$$ 5. **Factor the expression if needed:** $$9x^2 + 9x = 9x(x + 1)$$ This is the simplified form of the expression. The final answer is: $$9x^2 + 9x$$ or equivalently $$9x(x + 1)$$