Solve m=(m/a-n)(a+2)

$$m = ( \frac { m } { a } - n ) ( a + 2 )$$

Solve for m

$$m=\frac{an\left(a+2\right)}{2}$$

$$a\neq 0$$

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Multiply n times \frac{a}{a}.

$$m=\left(\frac{m}{a}-\frac{na}{a}\right)\left(a+2\right)$$

Since \frac{m}{a} and \frac{na}{a} have the same denominator, subtract them by subtracting their numerators.

$$m=\frac{m-na}{a}\left(a+2\right)$$

Express \frac{m-na}{a}\left(a+2\right) as a single fraction.

$$m=\frac{\left(m-na\right)\left(a+2\right)}{a}$$

Use the distributive property to multiply m-na by a+2.

$$m=\frac{ma+2m-na^{2}-2na}{a}$$

Subtract \frac{ma+2m-na^{2}-2na}{a} from both sides.

$$m-\frac{ma+2m-na^{2}-2na}{a}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply m times \frac{a}{a}.

$$\frac{ma}{a}-\frac{ma+2m-na^{2}-2na}{a}=0$$

Since \frac{ma}{a} and \frac{ma+2m-na^{2}-2na}{a} have the same denominator, subtract them by subtracting their numerators.

$$\frac{ma-\left(ma+2m-na^{2}-2na\right)}{a}=0$$

Do the multiplications in ma-\left(ma+2m-na^{2}-2na\right).

$$\frac{ma-ma-2m+na^{2}+2na}{a}=0$$

Combine like terms in ma-ma-2m+na^{2}+2na.

$$\frac{-2m+na^{2}+2na}{a}=0$$

Multiply both sides of the equation by a.

$$-2m+na^{2}+2na=0$$

Subtract na^{2} from both sides. Anything subtracted from zero gives its negation.

$$-2m+2na=-na^{2}$$

Subtract 2na from both sides.

$$-2m=-na^{2}-2na$$

The equation is in standard form.

$$-2m=-na^{2}-2an$$

Divide both sides by -2.

$$\frac{-2m}{-2}=-\frac{an\left(a+2\right)}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$m=-\frac{an\left(a+2\right)}{-2}$$

Divide -an\left(2+a\right) by -2.

$$m=\frac{an\left(a+2\right)}{2}$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{\sqrt{n\left(2m+n\right)}+n}{n}\text{, }&\left(arg(n)<\pi \text{ or }m\neq 0\right)\text{ and }n\neq 0\\a=\frac{\sqrt{n\left(2m+n\right)}-n}{n}\text{, }&\left(arg(n)\geq \pi \text{ or }m\neq 0\right)\text{ and }n\neq 0\\a\neq 0\text{, }&n=0\text{ and }m=0\end{matrix}\right.$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{\sqrt{n\left(2m+n\right)}+n}{n}\text{, }&\left(n\neq 0\text{ and }m=-\frac{n}{2}\right)\text{ or }\left(m\neq 0\text{ and }m\leq -\frac{n}{2}\text{ and }n<0\right)\text{ or }\left(n>0\text{ and }m\geq -\frac{n}{2}\right)\\a=\frac{\sqrt{n\left(2m+n\right)}-n}{n}\text{, }&\left(n\neq 0\text{ and }m=-\frac{n}{2}\right)\text{ or }\left(m\neq 0\text{ and }m\geq -\frac{n}{2}\text{ and }n>0\right)\text{ or }\left(n<0\text{ and }m\leq -\frac{n}{2}\right)\\a\neq 0\text{, }&n=0\text{ and }m=0\end{matrix}\right.$$