1. **State the problem:** Simplify the expression $-3x(x-1)$. 2. **Use the distributive property:** Multiply $-3x$ by each term inside the parentheses. The distributive property states $a(b+c) = ab + ac$. 3. **Apply the property:** $$-3x(x-1) = -3x \cdot x + (-3x) \cdot (-1)$$ 4. **Simplify each term:** $$-3x \cdot x = -3x^2$$ $$(-3x) \cdot (-1) = +3x$$ 5. **Combine the terms:** $$-3x^2 + 3x$$ 6. **Final answer:** $$\boxed{-3x^2 + 3x}$$