Solve y=exp(-t)

$$y = \exp ( - t )$$

Solve for p (complex solution)

$$\left\{\begin{matrix}p=-\frac{y}{etx}\text{, }&t\neq 0\text{ and }x\neq 0\\p\in \mathrm{C}\text{, }&\left(x=0\text{ or }t=0\right)\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$exp\left(-t\right)=y$$

Reorder the terms.

$$-eptx=y$$

The equation is in standard form.

$$\left(-etx\right)p=y$$

Divide both sides by -etx.

$$\frac{\left(-etx\right)p}{-etx}=\frac{y}{-etx}$$

Dividing by -etx undoes the multiplication by -etx.

$$p=\frac{y}{-etx}$$

Divide y by -etx.

$$p=-\frac{y}{etx}$$

Solve for t (complex solution)

$$\left\{\begin{matrix}t=-\frac{y}{epx}\text{, }&p\neq 0\text{ and }x\neq 0\\t\in \mathrm{C}\text{, }&\left(x=0\text{ or }p=0\right)\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$exp\left(-t\right)=y$$

Reorder the terms.

$$-eptx=y$$

The equation is in standard form.

$$\left(-epx\right)t=y$$

Divide both sides by -epx.

$$\frac{\left(-epx\right)t}{-epx}=\frac{y}{-epx}$$

Dividing by -epx undoes the multiplication by -epx.

$$t=\frac{y}{-epx}$$

Divide y by -epx.

$$t=-\frac{y}{epx}$$

Solve for p

$$\left\{\begin{matrix}p=-\frac{y}{etx}\text{, }&t\neq 0\text{ and }x\neq 0\\p\in \mathrm{R}\text{, }&\left(x=0\text{ or }t=0\right)\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$exp\left(-t\right)=y$$

Reorder the terms.

$$-eptx=y$$

The equation is in standard form.

$$\left(-etx\right)p=y$$

Divide both sides by -etx.

$$\frac{\left(-etx\right)p}{-etx}=\frac{y}{-etx}$$

Dividing by -etx undoes the multiplication by -etx.

$$p=\frac{y}{-etx}$$

Divide y by -etx.

$$p=-\frac{y}{etx}$$

Solve for t

$$\left\{\begin{matrix}t=-\frac{y}{epx}\text{, }&p\neq 0\text{ and }x\neq 0\\t\in \mathrm{R}\text{, }&\left(x=0\text{ or }p=0\right)\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$exp\left(-t\right)=y$$

Reorder the terms.

$$-eptx=y$$

The equation is in standard form.

$$\left(-epx\right)t=y$$

Divide both sides by -epx.

$$\frac{\left(-epx\right)t}{-epx}=\frac{y}{-epx}$$

Dividing by -epx undoes the multiplication by -epx.

$$t=\frac{y}{-epx}$$

Divide y by -epx.

$$t=-\frac{y}{epx}$$