Solve t=m/m_{0}*frac{P_{0}}{P}*t_{0}

$$t = \frac { m } { m _ { 0 } } \cdot \frac { P _ { 0 } } { P } \cdot t _ { 0 }$$

Solve for P_0 (complex solution)

$$\left\{\begin{matrix}P_{0}=\frac{Pm_{0}t}{mt_{0}}\text{, }&t_{0}\neq 0\text{ and }m\neq 0\text{ and }m_{0}\neq 0\text{ and }P\neq 0\\P_{0}\in \mathrm{C}\text{, }&\left(t_{0}=0\text{ or }m=0\right)\text{ and }t=0\text{ and }m_{0}\neq 0\text{ and }P\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by Pm_{0}, the least common multiple of m_{0},P.

$$tPm_{0}=Pm\times \frac{P_{0}}{P}t_{0}$$

Express P\times \frac{P_{0}}{P} as a single fraction.

$$tPm_{0}=\frac{PP_{0}}{P}mt_{0}$$

Cancel out P in both numerator and denominator.

$$tPm_{0}=P_{0}mt_{0}$$

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

$$P_{0}mt_{0}=tPm_{0}$$

The equation is in standard form.

$$mt_{0}P_{0}=Pm_{0}t$$

Divide both sides by mt_{0}.

$$\frac{mt_{0}P_{0}}{mt_{0}}=\frac{Pm_{0}t}{mt_{0}}$$

Dividing by mt_{0} undoes the multiplication by mt_{0}.

$$P_{0}=\frac{Pm_{0}t}{mt_{0}}$$

Solve for P_0

$$\left\{\begin{matrix}P_{0}=\frac{Pm_{0}t}{mt_{0}}\text{, }&t_{0}\neq 0\text{ and }m\neq 0\text{ and }m_{0}\neq 0\text{ and }P\neq 0\\P_{0}\in \mathrm{R}\text{, }&\left(t_{0}=0\text{ or }m=0\right)\text{ and }t=0\text{ and }m_{0}\neq 0\text{ and }P\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by Pm_{0}, the least common multiple of m_{0},P.

$$tPm_{0}=Pm\times \frac{P_{0}}{P}t_{0}$$

Express P\times \frac{P_{0}}{P} as a single fraction.

$$tPm_{0}=\frac{PP_{0}}{P}mt_{0}$$

Cancel out P in both numerator and denominator.

$$tPm_{0}=P_{0}mt_{0}$$

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

$$P_{0}mt_{0}=tPm_{0}$$

The equation is in standard form.

$$mt_{0}P_{0}=Pm_{0}t$$

Divide both sides by mt_{0}.

$$\frac{mt_{0}P_{0}}{mt_{0}}=\frac{Pm_{0}t}{mt_{0}}$$

Dividing by mt_{0} undoes the multiplication by mt_{0}.

$$P_{0}=\frac{Pm_{0}t}{mt_{0}}$$

Solve for P

$$\left\{\begin{matrix}P=\frac{P_{0}mt_{0}}{m_{0}t}\text{, }&t_{0}\neq 0\text{ and }P_{0}\neq 0\text{ and }m\neq 0\text{ and }m_{0}\neq 0\text{ and }t\neq 0\\P\neq 0\text{, }&\left(t_{0}=0\text{ or }P_{0}=0\text{ or }m=0\right)\text{ and }t=0\text{ and }m_{0}\neq 0\end{matrix}\right.$$