1. **State the problem:** Simplify the expression $$(12x^2+17x-4)+(9x^2-13x+3)$$. 2. **Remove parentheses:** Since both groups are added, we can remove the parentheses directly: $$12x^2 + 17x - 4 + 9x^2 - 13x + 3$$ 3. **Group like terms:** Group the terms with $x^2$, $x$, and constants: $$(12x^2 + 9x^2) + (17x - 13x) + (-4 + 3)$$ 4. **Simplify each group:** $$12x^2 + 9x^2 = 21x^2$$ $$17x - 13x = 4x$$ $$-4 + 3 = -1$$ 5. **Write the simplified expression:** $$21x^2 + 4x - 1$$ **Final answer:** $$21x^2 + 4x - 1$$