Solve a-w=akm^2

$$a - w = a k m ^ { 2 }$$

Solve for a

$$\left\{\begin{matrix}a=\frac{w}{1-km^{2}}\text{, }&m=0\text{ or }k\neq \frac{1}{m^{2}}\\a\in \mathrm{R}\text{, }&w=0\text{ and }k=\frac{1}{m^{2}}\text{ and }m\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract akm^{2} from both sides.

$$a-w-akm^{2}=0$$

Add w to both sides. Anything plus zero gives itself.

$$a-akm^{2}=w$$

Combine all terms containing a.

$$\left(1-km^{2}\right)a=w$$

Divide both sides by 1-km^{2}.

$$\frac{\left(1-km^{2}\right)a}{1-km^{2}}=\frac{w}{1-km^{2}}$$

Dividing by 1-km^{2} undoes the multiplication by 1-km^{2}.

$$a=\frac{w}{1-km^{2}}$$

Solve for k

$$\left\{\begin{matrix}k=-\frac{w-a}{am^{2}}\text{, }&m\neq 0\text{ and }a\neq 0\\k\in \mathrm{R}\text{, }&\left(a=w\text{ and }m=0\right)\text{ or }\left(a=0\text{ and }w=0\text{ and }m\neq 0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$akm^{2}=a-w$$

The equation is in standard form.

$$am^{2}k=a-w$$

Divide both sides by am^{2}.

$$\frac{am^{2}k}{am^{2}}=\frac{a-w}{am^{2}}$$

Dividing by am^{2} undoes the multiplication by am^{2}.

$$k=\frac{a-w}{am^{2}}$$