Solve 2x-pi/3=-pi/2+2kn

$$2 x - \frac { \pi } { 3 } = - \frac { \pi } { 2 } + 2 k n$$

Solve for k (complex solution)

$$\left\{\begin{matrix}k=\frac{12x+\pi }{12n}\text{, }&n\neq 0\\k\in \mathrm{C}\text{, }&x=-\frac{\pi }{12}\text{ and }n=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 3,2.

$$12x-2\pi =-3\pi +12kn$$

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

$$-3\pi +12kn=12x-2\pi$$

Add 3\pi to both sides.

$$12kn=12x-2\pi +3\pi$$

Combine -2\pi and 3\pi to get \pi .

$$12kn=12x+\pi$$

The equation is in standard form.

$$12nk=12x+\pi$$

Divide both sides by 12n.

$$\frac{12nk}{12n}=\frac{12x+\pi }{12n}$$

Dividing by 12n undoes the multiplication by 12n.

$$k=\frac{12x+\pi }{12n}$$

Solve for n (complex solution)

$$\left\{\begin{matrix}n=\frac{12x+\pi }{12k}\text{, }&k\neq 0\\n\in \mathrm{C}\text{, }&x=-\frac{\pi }{12}\text{ and }k=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 3,2.

$$12x-2\pi =-3\pi +12kn$$

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

$$-3\pi +12kn=12x-2\pi$$

Add 3\pi to both sides.

$$12kn=12x-2\pi +3\pi$$

Combine -2\pi and 3\pi to get \pi .

$$12kn=12x+\pi$$

Divide both sides by 12k.

$$\frac{12kn}{12k}=\frac{12x+\pi }{12k}$$

Dividing by 12k undoes the multiplication by 12k.

$$n=\frac{12x+\pi }{12k}$$

Solve for k

$$\left\{\begin{matrix}k=\frac{12x+\pi }{12n}\text{, }&n\neq 0\\k\in \mathrm{R}\text{, }&x=-\frac{\pi }{12}\text{ and }n=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 3,2.

$$12x-2\pi =-3\pi +12kn$$

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

$$-3\pi +12kn=12x-2\pi$$

Add 3\pi to both sides.

$$12kn=12x-2\pi +3\pi$$

Combine -2\pi and 3\pi to get \pi .

$$12kn=12x+\pi$$

The equation is in standard form.

$$12nk=12x+\pi$$

Divide both sides by 12n.

$$\frac{12nk}{12n}=\frac{12x+\pi }{12n}$$

Dividing by 12n undoes the multiplication by 12n.

$$k=\frac{12x+\pi }{12n}$$

Solve for n

$$\left\{\begin{matrix}n=\frac{12x+\pi }{12k}\text{, }&k\neq 0\\n\in \mathrm{R}\text{, }&x=-\frac{\pi }{12}\text{ and }k=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 3,2.

$$12x-2\pi =-3\pi +12kn$$

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

$$-3\pi +12kn=12x-2\pi$$

Add 3\pi to both sides.

$$12kn=12x-2\pi +3\pi$$

Combine -2\pi and 3\pi to get \pi .

$$12kn=12x+\pi$$

Divide both sides by 12k.

$$\frac{12kn}{12k}=\frac{12x+\pi }{12k}$$

Dividing by 12k undoes the multiplication by 12k.

$$n=\frac{12x+\pi }{12k}$$