Solve the equation by factoring. \[ 9 x^{2}+21 x-8=0 \] The solution set is \( \{\square\} \). (Use a comma to separate answers as needed. Type each solution only once.)

To solve the quadratic equation \( 9x^{2} + 21x - 8 = 0 \) by factoring, follow these steps: 1. **Find two numbers that multiply to \( 9 \times (-8) = -72 \) and add to \( 21 \).** The numbers are **24** and **-3** because: \[ 24 \times (-3) = -72 \quad \text{and} \quad 24 + (-3) = 21 \] 2. **Rewrite the middle term using these numbers:** \[ 9x^{2} + 24x - 3x - 8 = 0 \] 3. **Factor by grouping:** \[ (9x^{2} + 24x) + (-3x - 8) = 0 \] \[ 3x(3x + 8) -1(3x + 8) = 0 \] \[ (3x - 1)(3x + 8) = 0 \] 4. **Solve for \( x \):** \[ 3x - 1 = 0 \quad \Rightarrow \quad x = \frac{1}{3} \] \[ 3x + 8 = 0 \quad \Rightarrow \quad x = -\frac{8}{3} \] **Solution set:** \[ \left\{ \frac{1}{3}, -\frac{8}{3} \right\} \]