Solve by factoring or quadratic formula. \( 3 x^{2}+7 x=-2 \) \( x=\square \) \( * * * \) Use a reduced fraction or round to 3 decimals. List your answers separated by commas, for example: \( \frac{2}{3}, \frac{5}{2} \) type \( 2 / 3,5 / 2 \) Question Help:

\( 3x^2 + 7x + 2 = 0 \) We factor the quadratic by finding two numbers that multiply to \( 3 \times 2 = 6 \) and add to \( 7 \). The numbers \( 1 \) and \( 6 \) work since \( 1 \times 6 = 6 \) and \( 1 + 6 = 7 \). Rewrite the middle term: \[ 3x^2 + x + 6x + 2 = 0 \] Group the terms: \[ (3x^2 + x) + (6x + 2) = 0 \] Factor each group: \[ x(3x + 1) + 2(3x + 1) = 0 \] Factor out the common binomial: \[ (3x + 1)(x + 2) = 0 \] Set each factor equal to zero: \[ 3x + 1 = 0 \quad \text{or} \quad x + 2 = 0 \] Solve for \( x \): \[ x = -\frac{1}{3} \quad \text{or} \quad x = -2 \] Final answer: \( -1/3, -2 \)