Solve 12mk=3ek^2/5x+y

$$12 m k = \frac { 3 e k ^ { 2 } } { 5 x + y }$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=\frac{ek}{4\left(5x+y\right)}\text{, }&x\neq -\frac{y}{5}\\m\in \mathrm{C}\text{, }&k=0\text{ and }x\neq -\frac{y}{5}\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5x+y.

$$12mk\left(5x+y\right)=3ek^{2}$$

Use the distributive property to multiply 12mk by 5x+y.

$$60kmx+12mky=3ek^{2}$$

Combine all terms containing m.

$$\left(60kx+12ky\right)m=3ek^{2}$$

Divide both sides by 60kx+12ky.

$$\frac{\left(60kx+12ky\right)m}{60kx+12ky}=\frac{3ek^{2}}{60kx+12ky}$$

Dividing by 60kx+12ky undoes the multiplication by 60kx+12ky.

$$m=\frac{3ek^{2}}{60kx+12ky}$$

Divide 3ek^{2} by 60kx+12ky.

$$m=\frac{ek}{4\left(5x+y\right)}$$

Solve for m

$$\left\{\begin{matrix}m=\frac{ek}{4\left(5x+y\right)}\text{, }&x\neq -\frac{y}{5}\\m\in \mathrm{R}\text{, }&k=0\text{ and }x\neq -\frac{y}{5}\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5x+y.

$$12mk\left(5x+y\right)=3ek^{2}$$

Use the distributive property to multiply 12mk by 5x+y.

$$60kmx+12mky=3ek^{2}$$

Combine all terms containing m.

$$\left(60kx+12ky\right)m=3ek^{2}$$

Divide both sides by 60kx+12ky.

$$\frac{\left(60kx+12ky\right)m}{60kx+12ky}=\frac{3ek^{2}}{60kx+12ky}$$

Dividing by 60kx+12ky undoes the multiplication by 60kx+12ky.

$$m=\frac{3ek^{2}}{60kx+12ky}$$

Divide 3ek^{2} by 60kx+12ky.

$$m=\frac{ek}{4\left(5x+y\right)}$$

Solve for k

$$k=\frac{4m\left(5x+y\right)}{e}$$

$$k=0\text{, }x\neq -\frac{y}{5}$$