1. **State the problem:** We need to find the product of $-3x$ and $3x$. 2. **Formula used:** When multiplying two terms, multiply their coefficients (numbers) and then multiply the variables using the rule $x^a \times x^b = x^{a+b}$. 3. **Multiply coefficients:** $-3 \times 3 = -9$. 4. **Multiply variables:** $x \times x = x^{1+1} = x^2$. 5. **Combine results:** The product is $-9x^2$. 6. **Final answer:** $$-3x \times 3x = -9x^2$$