Solve E=Q/4pivarepsilon_{0varepsilon_{0}r^2}

$$E = \frac { Q } { 4 \pi \varepsilon _ { 0 } \varepsilon _ { 0 } r ^ { 2 } }$$

Solve for Q

$$Q=4\pi E\left(r\epsilon _{0}\right)^{2}$$

$$r\neq 0\text{ and }\epsilon _{0}\neq 0$$

Steps for Solving Linear Equation

Multiply \epsilon _{0} and \epsilon _{0} to get \epsilon _{0}^{2}.

$$E=\frac{Q}{4\pi \epsilon _{0}^{2}r^{2}}$$

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

$$\frac{Q}{4\pi \epsilon _{0}^{2}r^{2}}=E$$

The equation is in standard form.

$$\frac{1}{4\pi r^{2}\epsilon _{0}^{2}}Q=E$$

Divide both sides by \frac{1}{4}\pi ^{-1}\epsilon _{0}^{-2}r^{-2}.

$$\frac{\frac{1}{4\pi r^{2}\epsilon _{0}^{2}}Q\times 4\pi r^{2}\epsilon _{0}^{2}}{1}=\frac{E\times 4\pi r^{2}\epsilon _{0}^{2}}{1}$$

Dividing by \frac{1}{4}\pi ^{-1}\epsilon _{0}^{-2}r^{-2} undoes the multiplication by \frac{1}{4}\pi ^{-1}\epsilon _{0}^{-2}r^{-2}.

$$Q=\frac{E\times 4\pi r^{2}\epsilon _{0}^{2}}{1}$$

Divide E by \frac{1}{4}\pi ^{-1}\epsilon _{0}^{-2}r^{-2}.

$$Q=4\pi Er^{2}\epsilon _{0}^{2}$$

Solve for E

$$E=\frac{Q}{4\pi \left(r\epsilon _{0}\right)^{2}}$$

$$r\neq 0\text{ and }\epsilon _{0}\neq 0$$