Solve F=6.667*10^-11Nm/kg^2

$$F = 6.667 \times 10 ^ { - 11 } Nm / kg ^ { 2 }$$

Solve for N

$$\left\{\begin{matrix}N=\frac{100000000000000Fk}{6667mg^{2}}\text{, }&g\neq 0\text{ and }m\neq 0\text{ and }k\neq 0\\N\in \mathrm{R}\text{, }&\left(g=0\text{ or }m=0\right)\text{ and }F=0\text{ and }k\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by k.

$$Fk=6.667\times 10^{-11}Nmg^{2}$$

Calculate 10 to the power of -11 and get \frac{1}{100000000000}.

$$Fk=6.667\times \frac{1}{100000000000}Nmg^{2}$$

Multiply 6.667 and \frac{1}{100000000000} to get \frac{6667}{100000000000000}.

$$Fk=\frac{6667}{100000000000000}Nmg^{2}$$

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

$$\frac{6667}{100000000000000}Nmg^{2}=Fk$$

The equation is in standard form.

$$\frac{6667mg^{2}}{100000000000000}N=Fk$$

Divide both sides by \frac{6667}{100000000000000}mg^{2}.

$$\frac{100000000000000\times \frac{6667mg^{2}}{100000000000000}N}{6667mg^{2}}=\frac{100000000000000Fk}{6667mg^{2}}$$

Dividing by \frac{6667}{100000000000000}mg^{2} undoes the multiplication by \frac{6667}{100000000000000}mg^{2}.

$$N=\frac{100000000000000Fk}{6667mg^{2}}$$

Solve for F

$$F=\frac{6667Nmg^{2}}{100000000000000k}$$

$$k\neq 0$$