Solve PTAP=OK

$$P T A P = O K$$

Solve for A

$$\left\{\begin{matrix}A=\frac{KO}{TP^{2}}\text{, }&P\neq 0\text{ and }T\neq 0\\A\in \mathrm{R}\text{, }&\left(O=0\text{ and }P=0\right)\text{ or }\left(K=0\text{ and }P=0\right)\text{ or }\left(K=0\text{ and }T=0\text{ and }P\neq 0\right)\text{ or }\left(O=0\text{ and }T=0\text{ and }P\neq 0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply P and P to get P^{2}.

$$P^{2}TA=OK$$

The equation is in standard form.

$$TP^{2}A=KO$$

Divide both sides by P^{2}T.

$$\frac{TP^{2}A}{TP^{2}}=\frac{KO}{TP^{2}}$$

Dividing by P^{2}T undoes the multiplication by P^{2}T.

$$A=\frac{KO}{TP^{2}}$$

Solve for K

$$\left\{\begin{matrix}K=\frac{ATP^{2}}{O}\text{, }&O\neq 0\\K\in \mathrm{R}\text{, }&\left(T=0\text{ or }A=0\text{ or }P=0\right)\text{ and }O=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply P and P to get P^{2}.

$$P^{2}TA=OK$$

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

$$OK=P^{2}TA$$

The equation is in standard form.

$$OK=ATP^{2}$$

Divide both sides by O.

$$\frac{OK}{O}=\frac{ATP^{2}}{O}$$

Dividing by O undoes the multiplication by O.

$$K=\frac{ATP^{2}}{O}$$