Final answer:
The quadratic equation 4y² + 12y + 9 = 0 is best solved by recognizing it is a perfect square trinomial and factoring it into (2y + 3)(2y + 3) = 0, resulting in the solution y = -3/2.
Step-by-step explanation:
The question inquires about the most appropriate method to solve the quadratic equation: 4y² + 12y + 9 = 0. This equation can be solved in several ways, such as factoring, completing the square, graphing, or using the quadratic formula. However, one may observe that this specific equation has a particular structure that allows for a more straightforward approach. It is a perfect square trinomial because (2y + 3)² equals 4y² + 12y + 9. Therefore, the most appropriate method is factoring it into (2y + 3)(2y + 3) = 0, which leads to the solution y = -3/2.