Solve the following equation by factoring. \( 6\left(p^{2}-1\right)=5 p \) Rewrite the equation in a completely factored form. \( \begin{array}{l}(3 p+2)(2 p-3)=0 \\ \text { (Type your answer in factored form.) } \\ \text { The solution set is }\{\square\} \\ \text { (Simplify your answer. Type an integer or a simplified fraction. Use a comma to separate answers as needed.) }\end{array} \)

To solve the equation \( 6(p^2 - 1) = 5p \), first rewrite it in a standard form: 1. Expand the left side: \( 6p^2 - 6 = 5p \) 2. Bring all terms to one side: \( 6p^2 - 5p - 6 = 0 \) Next, we factor the quadratic equation \( 6p^2 - 5p - 6 \). This factors to: \[ (3p + 2)(2p - 3) = 0 \] To find the solution set, set each factor equal to zero: 1. \( 3p + 2 = 0 \) → \( p = -\frac{2}{3} \) 2. \( 2p - 3 = 0 \) → \( p = \frac{3}{2} \) Thus, the solution set is: \[ \left\{-\frac{2}{3}, \frac{3}{2}\right\} \]