1. **State the problem:** Simplify the expression $-5i(3 + 6i)$ and express the answer in terms of $i$. 2. **Recall the rule:** When multiplying complex numbers, distribute and use the fact that $i^2 = -1$. 3. **Apply distribution:** $$-5i(3 + 6i) = -5i \times 3 + (-5i) \times 6i = -15i - 30i^2$$ 4. **Simplify using $i^2 = -1$:** $$-15i - 30(-1) = -15i + 30$$ 5. **Write the final answer in standard form $a + bi$:** $$30 - 15i$$ Thus, the simplified expression is $30 - 15i$.