1. **State the problem:** Find the coefficient of $n$ in the expression $$(4n+3)(n+5) - (2n-3)^2.$$\n\n2. **Expand each part:**\n\nFirst, expand $$(4n+3)(n+5)$$ using distributive property:\n$$4n \cdot n + 4n \cdot 5 + 3 \cdot n + 3 \cdot 5 = 4n^2 + 20n + 3n + 15 = 4n^2 + 23n + 15.$$\n\nNext, expand $$(2n-3)^2$$ using the formula $$(a-b)^2 = a^2 - 2ab + b^2$$:\n$$ (2n)^2 - 2 \cdot 2n \cdot 3 + 3^2 = 4n^2 - 12n + 9.$$\n\n3. **Substitute expansions back into the expression:**\n$$ (4n^2 + 23n + 15) - (4n^2 - 12n + 9).$$\n\n4. **Simplify by subtracting:**\n$$4n^2 + 23n + 15 - 4n^2 + 12n - 9 = (4n^2 - 4n^2) + (23n + 12n) + (15 - 9) = 0 + 35n + 6 = 35n + 6.$$\n\n5. **Identify the coefficient of $n$:**\nThe coefficient of $n$ is **35**.