Solve (0)=2nr^2x-1

$$( 0 ) = 2 n r ^ { 2 } x - 1$$

Solve for n

$$n=\frac{1}{2xr^{2}}$$

$$x\neq 0\text{ and }r\neq 0$$

Steps for Solving Linear Equation

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

$$2nr^{2}x-1=0$$

Add 1 to both sides. Anything plus zero gives itself.

$$2nr^{2}x=1$$

The equation is in standard form.

$$2xr^{2}n=1$$

Divide both sides by 2r^{2}x.

$$\frac{2xr^{2}n}{2xr^{2}}=\frac{1}{2xr^{2}}$$

Dividing by 2r^{2}x undoes the multiplication by 2r^{2}x.

$$n=\frac{1}{2xr^{2}}$$

Solve for r (complex solution)

$$r=-\frac{\sqrt{2}n^{-\frac{1}{2}}x^{-\frac{1}{2}}}{2}$$

$$r=\frac{\sqrt{2}n^{-\frac{1}{2}}x^{-\frac{1}{2}}}{2}\text{, }x\neq 0\text{ and }n\neq 0$$

Solve for r

$$r=\frac{\sqrt{\frac{2}{nx}}}{2}$$

$$r=-\frac{\sqrt{\frac{2}{nx}}}{2}\text{, }\left(x>0\text{ and }n>0\right)\text{ or }\left(n<0\text{ and }x<0\right)$$