Solve 7m+2n=2m/p

$$7 m + 2 n = \frac { 2 m } { p }$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=-\frac{2np}{7p-2}\text{, }&p\neq \frac{2}{7}\text{ and }p\neq 0\\m\in \mathrm{C}\text{, }&p=\frac{2}{7}\text{ and }n=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by p.

$$7mp+2np=2m$$

Subtract 2m from both sides.

$$7mp+2np-2m=0$$

Subtract 2np from both sides. Anything subtracted from zero gives its negation.

$$7mp-2m=-2np$$

Combine all terms containing m.

$$\left(7p-2\right)m=-2np$$

Divide both sides by 7p-2.

$$\frac{\left(7p-2\right)m}{7p-2}=-\frac{2np}{7p-2}$$

Dividing by 7p-2 undoes the multiplication by 7p-2.

$$m=-\frac{2np}{7p-2}$$

Solve for m

$$\left\{\begin{matrix}m=-\frac{2np}{7p-2}\text{, }&p\neq \frac{2}{7}\text{ and }p\neq 0\\m\in \mathrm{R}\text{, }&p=\frac{2}{7}\text{ and }n=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by p.

$$7mp+2np=2m$$

Subtract 2m from both sides.

$$7mp+2np-2m=0$$

Subtract 2np from both sides. Anything subtracted from zero gives its negation.

$$7mp-2m=-2np$$

Combine all terms containing m.

$$\left(7p-2\right)m=-2np$$

Divide both sides by 7p-2.

$$\frac{\left(7p-2\right)m}{7p-2}=-\frac{2np}{7p-2}$$

Dividing by 7p-2 undoes the multiplication by 7p-2.

$$m=-\frac{2np}{7p-2}$$

Solve for n

$$n=-\frac{7m}{2}+\frac{m}{p}$$

$$p\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by p.

$$7mp+2np=2m$$

Subtract 7mp from both sides.

$$2np=2m-7mp$$

The equation is in standard form.

$$2pn=2m-7mp$$

Divide both sides by 2p.

$$\frac{2pn}{2p}=\frac{m\left(2-7p\right)}{2p}$$

Dividing by 2p undoes the multiplication by 2p.

$$n=\frac{m\left(2-7p\right)}{2p}$$

Divide m\left(2-7p\right) by 2p.

$$n=-\frac{7m}{2}+\frac{m}{p}$$