Solve for \( v \). \[ 4 v^{2}=-12 v-9 \] If there is more than one solution, separate them with commas (do not include spaces or variables). \[ v= \]

To solve the equation \( 4 v^{2} = -12 v - 9 \), we first rearrange it into standard quadratic form: \[ 4v^2 + 12v + 9 = 0 \] Now we'll divide the entire equation by 4 to make the coefficients smaller: \[ v^2 + 3v + \frac{9}{4} = 0 \] Next, we can use the quadratic formula \( v = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 1 \), \( b = 3 \), and \( c = \frac{9}{4} \). Calculating the discriminant: \[ b^2 - 4ac = 3^2 - 4 \cdot 1 \cdot \frac{9}{4} = 9 - 9 = 0 \] Since the discriminant is zero, there will be one unique solution: \[ v = \frac{-3 \pm \sqrt{0}}{2 \cdot 1} = \frac{-3}{2} \] Thus, the solution is: \[ v=-\frac{3}{2} \]