1. **State the problem:** We need to expand and simplify the expression $(-7x+2)(-3x-4)$. 2. **Formula used:** To multiply two binomials, use the distributive property (FOIL method): $$ (a+b)(c+d) = ac + ad + bc + bd $$ 3. **Apply the formula:** $$ (-7x)(-3x) + (-7x)(-4) + 2(-3x) + 2(-4) $$ 4. **Calculate each term:** $$ 21x^2 + 28x - 6x - 8 $$ 5. **Combine like terms:** $$ 21x^2 + (28x - 6x) - 8 $$ $$ 21x^2 + 22x - 8 $$ 6. **Final answer:** $$ \boxed{21x^2 + 22x - 8} $$