Solve F=w/2r(r+2)

$$F = \frac { w } { 2 r } ( r + 2 )$$

Solve for r

$$\left\{\begin{matrix}r=-\frac{2w}{w-2F}\text{, }&w\neq 0\text{ and }F\neq \frac{w}{2}\\r\neq 0\text{, }&F=0\text{ and }w=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable r cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2r.

$$F\times 2r=w\left(r+2\right)$$

Use the distributive property to multiply w by r+2.

$$F\times 2r=wr+2w$$

Subtract wr from both sides.

$$F\times 2r-wr=2w$$

Combine all terms containing r.

$$\left(F\times 2-w\right)r=2w$$

The equation is in standard form.

$$\left(2F-w\right)r=2w$$

Divide both sides by 2F-w.

$$\frac{\left(2F-w\right)r}{2F-w}=\frac{2w}{2F-w}$$

Dividing by 2F-w undoes the multiplication by 2F-w.

$$r=\frac{2w}{2F-w}$$

Variable r cannot be equal to 0.

$$r=\frac{2w}{2F-w}\text{, }r\neq 0$$

Solve for F

$$F=\frac{w}{2}+\frac{w}{r}$$

$$r\neq 0$$