1. **State the problem:** Simplify the expression $$(2x+3)^2 + 3x^2$$. 2. **Recall the formula:** The square of a binomial is given by $$(a+b)^2 = a^2 + 2ab + b^2$$. 3. **Apply the formula:** Here, $a=2x$ and $b=3$, so $$ (2x+3)^2 = (2x)^2 + 2 \cdot 2x \cdot 3 + 3^2 = 4x^2 + 12x + 9 $$ 4. **Rewrite the original expression:** $$ (2x+3)^2 + 3x^2 = 4x^2 + 12x + 9 + 3x^2 $$ 5. **Combine like terms:** $$ 4x^2 + 3x^2 = 7x^2 $$ 6. **Final simplified expression:** $$ 7x^2 + 12x + 9 $$ This is the simplified form of the given expression.