Solve z/3-3z/4=-5z/12-v

$$\frac { z } { 3 } - \frac { 3 z } { 4 } = - \frac { 5 z } { 12 } - v$$

Solve for v

$$v=0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 3,4,12.

$$4z-3\times 3z=-5z-12v$$

Multiply -3 and 3 to get -9.

$$4z-9z=-5z-12v$$

Combine 4z and -9z to get -5z.

$$-5z=-5z-12v$$

Swap sides so that all variable terms are on the left hand side.

$$-5z-12v=-5z$$

Add 5z to both sides.

$$-12v=-5z+5z$$

Combine -5z and 5z to get 0.

$$-12v=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since -12 is not equal to 0, v must be equal to 0.

$$v=0$$

Solve for z (complex solution)

$$z\in \mathrm{C}$$

$$v=0$$

Solve for z

$$z\in \mathrm{R}$$

$$v=0$$