Solve F=Kfrac{Q_{1}Q_{2}}{r_{2}}

$$F = K \frac { Q _ { 1 } Q _ { 2 } } { r _ { 2 } }$$

Solve for K

$$\left\{\begin{matrix}K=\frac{Fr_{2}}{Q_{1}Q_{2}}\text{, }&Q_{2}\neq 0\text{ and }Q_{1}\neq 0\text{ and }r_{2}\neq 0\\K\in \mathrm{R}\text{, }&\left(Q_{2}=0\text{ or }Q_{1}=0\right)\text{ and }F=0\text{ and }r_{2}\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by r_{2}.

$$Fr_{2}=KQ_{1}Q_{2}$$

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

$$KQ_{1}Q_{2}=Fr_{2}$$

The equation is in standard form.

$$Q_{1}Q_{2}K=Fr_{2}$$

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

$$\frac{Q_{1}Q_{2}K}{Q_{1}Q_{2}}=\frac{Fr_{2}}{Q_{1}Q_{2}}$$

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

$$K=\frac{Fr_{2}}{Q_{1}Q_{2}}$$

Solve for F

$$F=\frac{KQ_{1}Q_{2}}{r_{2}}$$

$$r_{2}\neq 0$$