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". \( v=\square \)

Solve the equation \( \frac{3}{2v-6}-2=-\frac{3}{v-3} \). Solve the equation by following steps: - step0: Solve for \(v\): \(\frac{3}{2v-6}-2=-\frac{3}{v-3}\) - step1: Find the domain: \(\frac{3}{2v-6}-2=-\frac{3}{v-3},v\neq 3\) - step2: Multiply both sides of the equation by LCD: \(\left(\frac{3}{2v-6}-2\right)\times 2\left(v-3\right)=-\frac{3}{v-3}\times 2\left(v-3\right)\) - step3: Simplify the equation: \(15-4v=-6\) - step4: Move the constant to the right side: \(-4v=-6-15\) - step5: Subtract the numbers: \(-4v=-21\) - step6: Change the signs: \(4v=21\) - step7: Divide both sides: \(\frac{4v}{4}=\frac{21}{4}\) - step8: Divide the numbers: \(v=\frac{21}{4}\) - step9: Check if the solution is in the defined range: \(v=\frac{21}{4},v\neq 3\) - step10: Find the intersection: \(v=\frac{21}{4}\) The solution to the equation \( \frac{3}{2v-6}-2=-\frac{3}{v-3} \) is \( v = \frac{21}{4} \) or \( v = 5.25 \).