Solve the equation for all values of \( x \) \[ -2(6 x+7)\left(x^{2}-2\right)=0 \]

To solve the equation \( -2(6 x + 7)(x^{2} - 2) = 0 \), we can set each factor to zero. First, we simplify the equation: 1. The equation is already factored: \( -2 \) is a constant and doesn't affect the roots, so we can ignore it. 2. Set the first factor to zero: \[ 6x + 7 = 0 \] \[ 6x = -7 \] \[ x = -\frac{7}{6} \] Next, set the second factor to zero: 1. \( x^{2} - 2 = 0 \) \[ x^{2} = 2 \] \[ x = \sqrt{2} \quad \text{or} \quad x = -\sqrt{2} \] So, the solutions to the equation \( -2(6 x + 7)(x^{2} - 2) = 0 \) are: \[ x = -\frac{7}{6}, \quad x = \sqrt{2}, \quad x = -\sqrt{2} \]