Solve for \( v \). \[ \frac{3}{2 v-6}-2=-\frac{3}{v-3} \] If there is more than one solution, separate them with commas. If there is no solution, click on "No solution". \( v=\square \)

To solve the equation \[ \frac{3}{2v-6} - 2 = -\frac{3}{v-3}, \] let's first simplify it. We can rewrite \(2v - 6\) as \(2(v - 3)\) to help with our denominators. The equation now becomes: \[ \frac{3}{2(v-3)} - 2 = -\frac{3}{v-3}. \] Next, multiply through by \(2(v-3)\) to eliminate the denominators: \[ 3 - 2 \cdot 2(v - 3) = -6. \] This simplifies to: \[ 3 - 4(v - 3) = -6. \] Distributing gives: \[ 3 - 4v + 12 = -6. \] Combining like terms results in: \[ 15 - 4v = -6. \] Now, isolate the \(v\) term: \[ -4v = -6 - 15 \\ -4v = -21. \] Dividing both sides by \(-4\) yields: \[ v = \frac{21}{4}. \] Therefore, the solution is: \( v = \frac{21}{4} \).