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

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

Solve for Q

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

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

Steps for Solving Linear Equation

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

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

The equation is in standard form.

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

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

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

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

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

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

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

Solve for E

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

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