Solve the quadratic equation by factoring. (Enter your answers as a comma-separated list.) \[ 3 x^{2}+9 x+6=0 \] \( x=\square \)

We begin with the quadratic equation: \[ 3x^2 + 9x + 6 = 0 \] **Step 1. Factor out the common factor.** Notice that \(3\) is a common factor in all the terms: \[ 3x^2 + 9x + 6 = 3(x^2 + 3x + 2) = 0 \] **Step 2. Factor the quadratic expression.** We now factor the quadratic inside the parentheses: \[ x^2 + 3x + 2 = (x + 1)(x + 2) \] **Step 3. Set the factors equal to zero and solve for \(x\).** Since \(3(x + 1)(x + 2) = 0\), we set each factor equal to zero: \[ x + 1 = 0 \quad \text{or} \quad x + 2 = 0 \] Thus, we have: \[ x = -1 \quad \text{or} \quad x = -2 \] **Final Answer:** \[ x = -1, \; -2 \]