Solve -2v/R^2+4piR=0

$$- \frac { 2 v } { R ^ { 2 } } + 4 \pi R = 0$$

Solve for v

$$v=2\pi R^{3}$$

$$R\neq 0$$

Steps for Solving Linear Equation

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

$$-2v+4\pi RR^{2}=0$$

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

$$-2v+4\pi R^{3}=0$$

Subtract 4\pi R^{3} from both sides. Anything subtracted from zero gives its negation.

$$-2v=-4\pi R^{3}$$

Divide both sides by -2.

$$\frac{-2v}{-2}=-\frac{4\pi R^{3}}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$v=-\frac{4\pi R^{3}}{-2}$$

Divide -4\pi R^{3} by -2.

$$v=2\pi R^{3}$$

Solve for R

$$R=\frac{2^{\frac{2}{3}}\sqrt[3]{\frac{v}{\pi }}}{2}$$

$$v\neq 0$$