1. **State the problem:** Expand the expression $ (7x-4)(x+9) $. 2. **Formula used:** Use the distributive property (also known as FOIL for binomials): $$ (a+b)(c+d) = ac + ad + bc + bd $$ 3. **Apply the formula:** $$ (7x-4)(x+9) = 7x \cdot x + 7x \cdot 9 - 4 \cdot x - 4 \cdot 9 $$ 4. **Calculate each term:** $$ 7x \cdot x = 7x^2 $$ $$ 7x \cdot 9 = 63x $$ $$ -4 \cdot x = -4x $$ $$ -4 \cdot 9 = -36 $$ 5. **Combine like terms:** $$ 7x^2 + 63x - 4x - 36 = 7x^2 + (63x - 4x) - 36 = 7x^2 + 59x - 36 $$ 6. **Final answer:** $$ \boxed{7x^2 + 59x - 36} $$