Solve -1/2kx=nk/5

$$- \frac { 1 } { 2 } k x = \frac { n k } { 5 }$$

Solve for k (complex solution)

$$\left\{\begin{matrix}\\k=0\text{, }&\text{unconditionally}\\k\in \mathrm{C}\text{, }&x=-\frac{2n}{5}\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 10, the least common multiple of 2,5.

$$-5kx=2nk$$

Subtract 2nk from both sides.

$$-5kx-2nk=0$$

Combine all terms containing k.

$$\left(-5x-2n\right)k=0$$

Divide 0 by -5x-2n.

$$k=0$$

Solve for n (complex solution)

$$\left\{\begin{matrix}\\n=-\frac{5x}{2}\text{, }&\text{unconditionally}\\n\in \mathrm{C}\text{, }&k=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 10, the least common multiple of 2,5.

$$-5kx=2nk$$

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

$$2nk=-5kx$$

The equation is in standard form.

$$2kn=-5kx$$

Divide both sides by 2k.

$$\frac{2kn}{2k}=-\frac{5kx}{2k}$$

Dividing by 2k undoes the multiplication by 2k.

$$n=-\frac{5kx}{2k}$$

Divide -5kx by 2k.

$$n=-\frac{5x}{2}$$

Solve for k

$$\left\{\begin{matrix}\\k=0\text{, }&\text{unconditionally}\\k\in \mathrm{R}\text{, }&x=-\frac{2n}{5}\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 10, the least common multiple of 2,5.

$$-5kx=2nk$$

Subtract 2nk from both sides.

$$-5kx-2nk=0$$

Combine all terms containing k.

$$\left(-5x-2n\right)k=0$$

Divide 0 by -5x-2n.

$$k=0$$

Solve for n

$$\left\{\begin{matrix}\\n=-\frac{5x}{2}\text{, }&\text{unconditionally}\\n\in \mathrm{R}\text{, }&k=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 10, the least common multiple of 2,5.

$$-5kx=2nk$$

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

$$2nk=-5kx$$

The equation is in standard form.

$$2kn=-5kx$$

Divide both sides by 2k.

$$\frac{2kn}{2k}=-\frac{5kx}{2k}$$

Dividing by 2k undoes the multiplication by 2k.

$$n=-\frac{5kx}{2k}$$

Divide -5kx by 2k.

$$n=-\frac{5x}{2}$$