Solve 12m-4n/5=mn+2n

$$\frac { 12 m - 4 n } { 5 } = m n + 2 n$$

Solve for m

$$m=\frac{14n}{12-5n}$$

$$n\neq \frac{12}{5}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5.

$$12m-4n=5mn+10n$$

Subtract 5mn from both sides.

$$12m-4n-5mn=10n$$

Add 4n to both sides.

$$12m-5mn=10n+4n$$

Combine 10n and 4n to get 14n.

$$12m-5mn=14n$$

Combine all terms containing m.

$$\left(12-5n\right)m=14n$$

Divide both sides by 12-5n.

$$\frac{\left(12-5n\right)m}{12-5n}=\frac{14n}{12-5n}$$

Dividing by 12-5n undoes the multiplication by 12-5n.

$$m=\frac{14n}{12-5n}$$

Solve for n

$$n=\frac{12m}{5m+14}$$

$$m\neq -\frac{14}{5}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5.

$$12m-4n=5mn+10n$$

Subtract 5mn from both sides.

$$12m-4n-5mn=10n$$

Subtract 10n from both sides.

$$12m-4n-5mn-10n=0$$

Combine -4n and -10n to get -14n.

$$12m-14n-5mn=0$$

Subtract 12m from both sides. Anything subtracted from zero gives its negation.

$$-14n-5mn=-12m$$

Combine all terms containing n.

$$\left(-14-5m\right)n=-12m$$

The equation is in standard form.

$$\left(-5m-14\right)n=-12m$$

Divide both sides by -14-5m.

$$\frac{\left(-5m-14\right)n}{-5m-14}=-\frac{12m}{-5m-14}$$

Dividing by -14-5m undoes the multiplication by -14-5m.

$$n=-\frac{12m}{-5m-14}$$

Divide -12m by -14-5m.

$$n=\frac{12m}{5m+14}$$