Solve F=gfrac{m_{1}m_{2}}{r^2}

$$F = g \frac { m _ { 1 } m _ { 2 } } { r ^ { 2 } }$$

Solve for g (complex solution)

$$\left\{\begin{matrix}g=\frac{Fr^{2}}{m_{1}m_{2}}\text{, }&m_{2}\neq 0\text{ and }m_{1}\neq 0\text{ and }r\neq 0\\g\in \mathrm{C}\text{, }&\left(m_{2}=0\text{ or }m_{1}=0\right)\text{ and }F=0\text{ and }r\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$Fr^{2}=gm_{1}m_{2}$$

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

$$gm_{1}m_{2}=Fr^{2}$$

The equation is in standard form.

$$m_{1}m_{2}g=Fr^{2}$$

Divide both sides by m_{1}m_{2}.

$$\frac{m_{1}m_{2}g}{m_{1}m_{2}}=\frac{Fr^{2}}{m_{1}m_{2}}$$

Dividing by m_{1}m_{2} undoes the multiplication by m_{1}m_{2}.

$$g=\frac{Fr^{2}}{m_{1}m_{2}}$$

Solve for g

$$\left\{\begin{matrix}g=\frac{Fr^{2}}{m_{1}m_{2}}\text{, }&m_{2}\neq 0\text{ and }m_{1}\neq 0\text{ and }r\neq 0\\g\in \mathrm{R}\text{, }&\left(m_{2}=0\text{ or }m_{1}=0\right)\text{ and }F=0\text{ and }r\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$Fr^{2}=gm_{1}m_{2}$$

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

$$gm_{1}m_{2}=Fr^{2}$$

The equation is in standard form.

$$m_{1}m_{2}g=Fr^{2}$$

Divide both sides by m_{1}m_{2}.

$$\frac{m_{1}m_{2}g}{m_{1}m_{2}}=\frac{Fr^{2}}{m_{1}m_{2}}$$

Dividing by m_{1}m_{2} undoes the multiplication by m_{1}m_{2}.

$$g=\frac{Fr^{2}}{m_{1}m_{2}}$$

Solve for F

$$F=\frac{gm_{1}m_{2}}{r^{2}}$$

$$r\neq 0$$