1. **State the problem:** Simplify the expression $ (2x+3) + (4x-5)(2x+3) + (4x-5) $. 2. **Recall the distributive property:** To simplify expressions with parentheses, multiply terms inside the parentheses and then combine like terms. 3. **Apply the distributive property to** $(4x-5)(2x+3)$: $$ (4x-5)(2x+3) = 4x \cdot 2x + 4x \cdot 3 - 5 \cdot 2x - 5 \cdot 3 = 8x^2 + 12x - 10x - 15 $$ 4. **Simplify the multiplication result:** $$ 8x^2 + (12x - 10x) - 15 = 8x^2 + 2x - 15 $$ 5. **Rewrite the original expression substituting the expanded form:** $$ (2x+3) + (8x^2 + 2x - 15) + (4x - 5) $$ 6. **Combine like terms:** - Combine $x^2$ terms: $8x^2$ - Combine $x$ terms: $2x + 2x + 4x = 8x$ - Combine constants: $3 - 15 - 5 = -17$ 7. **Final simplified expression:** $$ 8x^2 + 8x - 17 $$ This is the simplified form of the given expression.