Solve \( (-3 z-1)^{2}-9=0 \) List them separated by commas, for example: \( \frac{2}{3}, \frac{5}{2} \) type " \( 2 / 3,5 / 2^{\text {" }} \)

Let's start by rearranging the equation: \[ (-3z - 1)^{2} - 9 = 0 \] This can be rewritten as: \[ (-3z - 1)^{2} = 9 \] Taking the square root of both sides yields: \[ -3z - 1 = 3 \quad \text{or} \quad -3z - 1 = -3 \] Now let's solve both equations: 1. For \( -3z - 1 = 3 \): \[ -3z = 3 + 1 \implies -3z = 4 \implies z = -\frac{4}{3} \] 2. For \( -3z - 1 = -3 \): \[ -3z = -3 + 1 \implies -3z = -2 \implies z = \frac{2}{3} \] Thus, the solutions are: \[ -\frac{4}{3}, \frac{2}{3} \]