Chapter 4 Quadratic Functions and Factoring - 4.8 Use the Quadratic Formula and the Discriminant - 4.8 Exercises - Skill Practice - Page 296: 22

$$z=-7,\:z=-8$$

Solving the equation using the quadratic formula, we find: $$z_{1,\:2}=\frac{-15\pm \sqrt{15^2-4\cdot \:1\cdot \:56}}{2\cdot \:1} \\ z=-7,\:z=-8$$ Checking by factoring the expression, we find: $$z\left(z+7\right)+8\left(z+7\right) \\ \left(z+7\right)\left(z+8\right)$$