Solve 9mn-k=6kn

$$9 m n - k = 6 k n$$

Solve for k

$$\left\{\begin{matrix}k=\frac{9mn}{6n+1}\text{, }&n\neq -\frac{1}{6}\\k\in \mathrm{R}\text{, }&m=0\text{ and }n=-\frac{1}{6}\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 6kn from both sides.

$$9mn-k-6kn=0$$

Subtract 9mn from both sides. Anything subtracted from zero gives its negation.

$$-k-6kn=-9mn$$

Combine all terms containing k.

$$\left(-1-6n\right)k=-9mn$$

The equation is in standard form.

$$\left(-6n-1\right)k=-9mn$$

Divide both sides by -1-6n.

$$\frac{\left(-6n-1\right)k}{-6n-1}=-\frac{9mn}{-6n-1}$$

Dividing by -1-6n undoes the multiplication by -1-6n.

$$k=-\frac{9mn}{-6n-1}$$

Divide -9mn by -1-6n.

$$k=\frac{9mn}{6n+1}$$

Solve for m

$$\left\{\begin{matrix}m=\frac{2k}{3}+\frac{k}{9n}\text{, }&n\neq 0\\m\in \mathrm{R}\text{, }&k=0\text{ and }n=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add k to both sides.

$$9mn=6kn+k$$

The equation is in standard form.

$$9nm=6kn+k$$

Divide both sides by 9n.

$$\frac{9nm}{9n}=\frac{6kn+k}{9n}$$

Dividing by 9n undoes the multiplication by 9n.

$$m=\frac{6kn+k}{9n}$$

Divide 6kn+k by 9n.

$$m=\frac{2k}{3}+\frac{k}{9n}$$