1. **State the problem:** We need to expand and simplify the expression $$(4x-11)(-x+2)$$. 2. **Recall the distributive property:** To multiply two binomials, multiply each term in the first binomial by each term in the second binomial. 3. **Apply the distributive property:** $$ (4x-11)(-x+2) = 4x \cdot (-x) + 4x \cdot 2 - 11 \cdot (-x) - 11 \cdot 2 $$ 4. **Calculate each product:** $$ 4x \cdot (-x) = -4x^2 $$ $$ 4x \cdot 2 = 8x $$ $$ -11 \cdot (-x) = +11x $$ $$ -11 \cdot 2 = -22 $$ 5. **Combine all terms:** $$ -4x^2 + 8x + 11x - 22 $$ 6. **Simplify like terms:** $$ 8x + 11x = 19x $$ 7. **Final simplified expression:** $$ \boxed{-4x^2 + 19x - 22} $$ This is the expanded and simplified form of the given expression.