Solve z=v-p/sf

$$z = \frac { v - p } { s } f$$

Solve for f

$$\left\{\begin{matrix}f=\frac{sz}{v-p}\text{, }&v\neq p\text{ and }s\neq 0\\f\in \mathrm{R}\text{, }&z=0\text{ and }v=p\text{ and }s\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by s.

$$zs=\left(v-p\right)f$$

Use the distributive property to multiply v-p by f.

$$zs=vf-pf$$

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

$$vf-pf=zs$$

Combine all terms containing f.

$$\left(v-p\right)f=zs$$

The equation is in standard form.

$$\left(v-p\right)f=sz$$

Divide both sides by v-p.

$$\frac{\left(v-p\right)f}{v-p}=\frac{sz}{v-p}$$

Dividing by v-p undoes the multiplication by v-p.

$$f=\frac{sz}{v-p}$$

Solve for p

$$\left\{\begin{matrix}p=-\frac{sz}{f}+v\text{, }&s\neq 0\text{ and }f\neq 0\\p\in \mathrm{R}\text{, }&z=0\text{ and }f=0\text{ and }s\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by s.

$$zs=\left(v-p\right)f$$

Use the distributive property to multiply v-p by f.

$$zs=vf-pf$$

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

$$vf-pf=zs$$

Subtract vf from both sides.

$$-pf=zs-vf$$

The equation is in standard form.

$$\left(-f\right)p=sz-fv$$

Divide both sides by -f.

$$\frac{\left(-f\right)p}{-f}=\frac{sz-fv}{-f}$$

Dividing by -f undoes the multiplication by -f.

$$p=\frac{sz-fv}{-f}$$

Divide zs-vf by -f.

$$p=-\frac{sz}{f}+v$$