Solve (E=1/4piepsilon_{0}q/r^2)

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

Solve for q

$$q=4\pi Eϵ_{0}r^{2}$$

$$ϵ_{0}\neq 0\text{ and }r\neq 0$$

Steps for Solving Linear Equation

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

$$Er^{2}=\frac{1}{4}r^{2}\left(\pi ϵ_{0}\right)^{-1}\times 1\times \frac{q}{r^{2}}$$

Expand \left(\pi ϵ_{0}\right)^{-1}.

$$Er^{2}=\frac{1}{4}r^{2}\pi ^{-1}ϵ_{0}^{-1}\times 1\times \frac{q}{r^{2}}$$

Multiply \frac{1}{4} and 1 to get \frac{1}{4}.

$$Er^{2}=\frac{1}{4}r^{2}\pi ^{-1}ϵ_{0}^{-1}\times \frac{q}{r^{2}}$$

Multiply \frac{1}{4} times \frac{q}{r^{2}} by multiplying numerator times numerator and denominator times denominator.

$$Er^{2}=\frac{q}{4r^{2}}r^{2}\pi ^{-1}ϵ_{0}^{-1}$$

Express \frac{q}{4r^{2}}r^{2} as a single fraction.

$$Er^{2}=\frac{qr^{2}}{4r^{2}}\pi ^{-1}ϵ_{0}^{-1}$$

Cancel out r^{2} in both numerator and denominator.

$$Er^{2}=\frac{q}{4}\pi ^{-1}ϵ_{0}^{-1}$$

Express \frac{q}{4}\pi ^{-1} as a single fraction.

$$Er^{2}=\frac{q\pi ^{-1}}{4}ϵ_{0}^{-1}$$

Express \frac{q\pi ^{-1}}{4}ϵ_{0}^{-1} as a single fraction.

$$Er^{2}=\frac{q\pi ^{-1}ϵ_{0}^{-1}}{4}$$

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

$$\frac{q\pi ^{-1}ϵ_{0}^{-1}}{4}=Er^{2}$$

Multiply both sides of the equation by 4.

$$q\pi ^{-1}ϵ_{0}^{-1}=4Er^{2}$$

Reorder the terms.

$$\frac{1}{\pi }\times \frac{1}{ϵ_{0}}q=4Er^{2}$$

Multiply both sides of the equation by ϵ_{0}.

$$ϵ_{0}\pi ^{-1}\times 1\times \frac{1}{ϵ_{0}}q=4Er^{2}ϵ_{0}$$

Express ϵ_{0}\times \frac{1}{ϵ_{0}} as a single fraction.

$$\frac{ϵ_{0}}{ϵ_{0}}\pi ^{-1}\times 1q=4Er^{2}ϵ_{0}$$

Cancel out ϵ_{0} in both numerator and denominator.

$$1\pi ^{-1}\times 1q=4Er^{2}ϵ_{0}$$

Multiply 1 and 1 to get 1.

$$\pi ^{-1}q=4Er^{2}ϵ_{0}$$

Reorder the terms.

$$\frac{1}{\pi }q=4Eϵ_{0}r^{2}$$

Divide both sides by \pi ^{-1}.

$$\frac{\frac{1}{\pi }q\pi }{1}=\frac{4Eϵ_{0}r^{2}\pi }{1}$$

Dividing by \pi ^{-1} undoes the multiplication by \pi ^{-1}.

$$q=\frac{4Eϵ_{0}r^{2}\pi }{1}$$

Divide 4Eϵ_{0}r^{2} by \pi ^{-1}.

$$q=4\pi Eϵ_{0}r^{2}$$

Solve for E

$$E=\frac{q}{4\pi ϵ_{0}r^{2}}$$

$$ϵ_{0}\neq 0\text{ and }r\neq 0$$