Solve F=gmM/d^2

$$F = g \frac { m M } { d ^ { 2 } }$$

Solve for M (complex solution)

$$\left\{\begin{matrix}M=\frac{Fd^{2}}{gm}\text{, }&m\neq 0\text{ and }g\neq 0\text{ and }d\neq 0\\M\in \mathrm{C}\text{, }&\left(m=0\text{ or }g=0\right)\text{ and }F=0\text{ and }d\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$Fd^{2}=gmM$$

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

$$gmM=Fd^{2}$$

Divide both sides by gm.

$$\frac{gmM}{gm}=\frac{Fd^{2}}{gm}$$

Dividing by gm undoes the multiplication by gm.

$$M=\frac{Fd^{2}}{gm}$$

Solve for M

$$\left\{\begin{matrix}M=\frac{Fd^{2}}{gm}\text{, }&m\neq 0\text{ and }g\neq 0\text{ and }d\neq 0\\M\in \mathrm{R}\text{, }&\left(m=0\text{ or }g=0\right)\text{ and }F=0\text{ and }d\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$Fd^{2}=gmM$$

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

$$gmM=Fd^{2}$$

Divide both sides by gm.

$$\frac{gmM}{gm}=\frac{Fd^{2}}{gm}$$

Dividing by gm undoes the multiplication by gm.

$$M=\frac{Fd^{2}}{gm}$$

Solve for F

$$F=\frac{Mgm}{d^{2}}$$

$$d\neq 0$$