Solve v=p(1-d%)

$$v = p ( 1 - d \% )$$

Solve for d

$$\left\{\begin{matrix}d=-\frac{100v}{p}+100\text{, }&p\neq 0\\d\in \mathrm{R}\text{, }&v=0\text{ and }p=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply p by 1-\frac{d}{100}.

$$v=p+p\left(-\frac{d}{100}\right)$$

Express p\left(-\frac{d}{100}\right) as a single fraction.

$$v=p+\frac{-pd}{100}$$

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

$$p+\frac{-pd}{100}=v$$

Subtract p from both sides.

$$\frac{-pd}{100}=v-p$$

Multiply both sides of the equation by 100.

$$-pd=100v-100p$$

The equation is in standard form.

$$\left(-p\right)d=100v-100p$$

Divide both sides by -p.

$$\frac{\left(-p\right)d}{-p}=\frac{100v-100p}{-p}$$

Dividing by -p undoes the multiplication by -p.

$$d=\frac{100v-100p}{-p}$$

Divide 100v-100p by -p.

$$d=-\frac{100v}{p}+100$$

Solve for p

$$\left\{\begin{matrix}p=-\frac{100v}{d-100}\text{, }&d\neq 100\\p\in \mathrm{R}\text{, }&v=0\text{ and }d=100\end{matrix}\right.$$