Solve 4nD=4/n^2

$$4 n D = \frac { 4 } { n ^ { 2 } }$$

Solve for D

$$D=\frac{1}{n^{3}}$$

$$n\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by n^{2}.

$$4nDn^{2}=4$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$4n^{3}D=4$$

Divide both sides by 4n^{3}.

$$\frac{4n^{3}D}{4n^{3}}=\frac{4}{4n^{3}}$$

Dividing by 4n^{3} undoes the multiplication by 4n^{3}.

$$D=\frac{4}{4n^{3}}$$

Divide 4 by 4n^{3}.

$$D=\frac{1}{n^{3}}$$

Solve for n (complex solution)

$$n=e^{\frac{2\pi i}{3}}D^{-\frac{1}{3}}$$

$$n=D^{-\frac{1}{3}}$$

$$n=e^{\frac{4\pi i}{3}}D^{-\frac{1}{3}}\text{, }D\neq 0$$

Solve for n

$$n=\frac{1}{\sqrt[3]{D}}$$

$$D\neq 0$$