Solve the equation. (Enter your answers as a comma-separated list.) \[ p(p+1)=56 \] SUBMIT ANSWER

We start with the equation \[ p(p+1)=56. \] Expanding the left-hand side, we obtain \[ p^2+p=56. \] Subtract \(56\) from both sides to rewrite the equation in standard quadratic form: \[ p^2+p-56=0. \] Next, we factor the quadratic equation. We look for two numbers whose product is \(-56\) and sum is \(1\). These numbers are \(8\) and \(-7\), because \[ 8 \times (-7) = -56 \quad \text{and} \quad 8 + (-7) = 1. \] Thus, we can factor the quadratic as: \[ (p+8)(p-7)=0. \] Setting each factor equal to zero gives the solutions: \[ p+8=0 \quad \text{or} \quad p-7=0. \] Solving these, we find: \[ p=-8 \quad \text{or} \quad p=7. \] So, the solutions are: \[ 7, -8. \]