1. **State the problem:** Simplify the expression $3(2i - i) + i(5 + 2i)$ and write it in the form $x + yi$ where $x$ and $y$ are real numbers. 2. **Recall the rules:** - $i$ is the imaginary unit with the property $i^2 = -1$. - Distribute multiplication over addition. - Combine like terms (real parts and imaginary parts separately). 3. **Simplify inside the parentheses:** $$3(2i - i) = 3(i) = 3i$$ 4. **Distribute $i$ in the second term:** $$i(5 + 2i) = i \cdot 5 + i \cdot 2i = 5i + 2i^2$$ 5. **Replace $i^2$ with $-1$:** $$5i + 2(-1) = 5i - 2$$ 6. **Combine all terms:** $$3i + (5i - 2) = (0 - 2) + (3i + 5i) = -2 + 8i$$ 7. **Final answer:** $$\boxed{-2 + 8i}$$