Solve the following equation by factoring. \( z^{2}+2 z-15=0 \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is \( \} \) (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There is no solution.

To solve the quadratic equation \( z^{2} + 2z - 15 = 0 \) by factoring, follow these steps: 1. **Find two numbers that multiply to \(-15\) and add up to \(2\).** - The numbers \(5\) and \(-3\) satisfy this condition because: \[ 5 \times (-3) = -15 \quad \text{and} \quad 5 + (-3) = 2 \] 2. **Factor the quadratic equation using these numbers:** \[ z^{2} + 2z - 15 = (z + 5)(z - 3) = 0 \] 3. **Set each factor equal to zero and solve for \(z\):** - \(z + 5 = 0 \Rightarrow z = -5\) - \(z - 3 = 0 \Rightarrow z = 3\) Therefore, the solution set is \(\{-5, 3\}\). **Answer:** **A. The solution set is \(\{-5, 3\}\)**