1. **State the problem:** Simplify the expression $4(a-5)+2(5-a)$.\n\n2. **Recall the distributive property:** $k(x+y) = kx + ky$. We will apply this to both terms.\n\n3. **Distribute:**\n$$4(a-5) = 4a - 20$$\n$$2(5-a) = 10 - 2a$$\n\n4. **Rewrite the expression:**\n$$4a - 20 + 10 - 2a$$\n\n5. **Combine like terms:**\n$$4a - 2a = 2a$$\n$$-20 + 10 = -10$$\n\n6. **Final simplified expression:**\n$$2a - 10$$