Solve Q=S*[(1/n)-(1/10000)-(e-R)]

$$Q = S \cdot [ ( 1 / n ) - ( 1 / 10000 ) - ( e - R ) ]$$

Solve for R (complex solution)

$$\left\{\begin{matrix}R=\frac{Sn+10000eSn+10000Qn-10000S}{10000Sn}\text{, }&S\neq 0\text{ and }n\neq 0\\R\in \mathrm{C}\text{, }&Q=0\text{ and }S=0\text{ and }n\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 10000n, the least common multiple of n,10000.

$$Q\times 10000n=S\left(\frac{1}{n}-\frac{1}{10000}-\left(e-R\right)\right)\times 10000n$$

To find the opposite of e-R, find the opposite of each term.

$$Q\times 10000n=S\left(\frac{1}{n}-\frac{1}{10000}-e+R\right)\times 10000n$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of n and 10000 is 10000n. Multiply \frac{1}{n} times \frac{10000}{10000}. Multiply \frac{1}{10000} times \frac{n}{n}.

$$Q\times 10000n=S\left(\frac{10000}{10000n}-\frac{n}{10000n}-e+R\right)\times 10000n$$

Since \frac{10000}{10000n} and \frac{n}{10000n} have the same denominator, subtract them by subtracting their numerators.

$$Q\times 10000n=S\left(\frac{10000-n}{10000n}-e+R\right)\times 10000n$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -e+R times \frac{10000n}{10000n}.

$$Q\times 10000n=S\left(\frac{10000-n}{10000n}+\frac{\left(-e+R\right)\times 10000n}{10000n}\right)\times 10000n$$

Since \frac{10000-n}{10000n} and \frac{\left(-e+R\right)\times 10000n}{10000n} have the same denominator, add them by adding their numerators.

$$Q\times 10000n=S\times \frac{10000-n+\left(-e+R\right)\times 10000n}{10000n}\times 10000n$$

Do the multiplications in 10000-n+\left(-e+R\right)\times 10000n.

$$Q\times 10000n=S\times \frac{10000-n-10000en+10000Rn}{10000n}\times 10000n$$

Express S\times \frac{10000-n-10000en+10000Rn}{10000n} as a single fraction.

$$Q\times 10000n=\frac{S\left(10000-n-10000en+10000Rn\right)}{10000n}\times 10000n$$

Express \frac{S\left(10000-n-10000en+10000Rn\right)}{10000n}\times 10000 as a single fraction.

$$Q\times 10000n=\frac{S\left(10000-n-10000en+10000Rn\right)\times 10000}{10000n}n$$

Cancel out 10000 in both numerator and denominator.

$$Q\times 10000n=\frac{S\left(10000Rn-10000en-n+10000\right)}{n}n$$

Express \frac{S\left(10000Rn-10000en-n+10000\right)}{n}n as a single fraction.

$$Q\times 10000n=\frac{S\left(10000Rn-10000en-n+10000\right)n}{n}$$

Cancel out n in both numerator and denominator.

$$Q\times 10000n=S\left(10000Rn-10000en-n+10000\right)$$

Use the distributive property to multiply S by 10000Rn-10000en-n+10000.

$$Q\times 10000n=10000SRn-10000Sen-Sn+10000S$$

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

$$10000SRn-10000Sen-Sn+10000S=Q\times 10000n$$

Add 10000Sen to both sides.

$$10000SRn-Sn+10000S=Q\times 10000n+10000Sen$$

Add Sn to both sides.

$$10000SRn+10000S=Q\times 10000n+10000Sen+Sn$$

Subtract 10000S from both sides.

$$10000SRn=Q\times 10000n+10000Sen+Sn-10000S$$

The equation is in standard form.

$$10000SnR=Sn+10000eSn+10000Qn-10000S$$

Divide both sides by 10000Sn.

$$\frac{10000SnR}{10000Sn}=\frac{Sn+10000eSn+10000Qn-10000S}{10000Sn}$$

Dividing by 10000Sn undoes the multiplication by 10000Sn.

$$R=\frac{Sn+10000eSn+10000Qn-10000S}{10000Sn}$$

Divide 10000Qn+10000Sen+Sn-10000S by 10000Sn.

$$R=\frac{Q}{S}+e+\frac{1}{10000}-\frac{1}{n}$$

Solve for R

$$\left\{\begin{matrix}R=\frac{Sn+10000eSn+10000Qn-10000S}{10000Sn}\text{, }&S\neq 0\text{ and }n\neq 0\\R\in \mathrm{R}\text{, }&Q=0\text{ and }S=0\text{ and }n\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 10000n, the least common multiple of n,10000.

$$Q\times 10000n=S\left(\frac{1}{n}-\frac{1}{10000}-\left(e-R\right)\right)\times 10000n$$

To find the opposite of e-R, find the opposite of each term.

$$Q\times 10000n=S\left(\frac{1}{n}-\frac{1}{10000}-e+R\right)\times 10000n$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of n and 10000 is 10000n. Multiply \frac{1}{n} times \frac{10000}{10000}. Multiply \frac{1}{10000} times \frac{n}{n}.

$$Q\times 10000n=S\left(\frac{10000}{10000n}-\frac{n}{10000n}-e+R\right)\times 10000n$$

Since \frac{10000}{10000n} and \frac{n}{10000n} have the same denominator, subtract them by subtracting their numerators.

$$Q\times 10000n=S\left(\frac{10000-n}{10000n}-e+R\right)\times 10000n$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -e+R times \frac{10000n}{10000n}.

$$Q\times 10000n=S\left(\frac{10000-n}{10000n}+\frac{\left(-e+R\right)\times 10000n}{10000n}\right)\times 10000n$$

Since \frac{10000-n}{10000n} and \frac{\left(-e+R\right)\times 10000n}{10000n} have the same denominator, add them by adding their numerators.

$$Q\times 10000n=S\times \frac{10000-n+\left(-e+R\right)\times 10000n}{10000n}\times 10000n$$

Do the multiplications in 10000-n+\left(-e+R\right)\times 10000n.

$$Q\times 10000n=S\times \frac{10000-n-10000en+10000Rn}{10000n}\times 10000n$$

Express S\times \frac{10000-n-10000en+10000Rn}{10000n} as a single fraction.

$$Q\times 10000n=\frac{S\left(10000-n-10000en+10000Rn\right)}{10000n}\times 10000n$$

Express \frac{S\left(10000-n-10000en+10000Rn\right)}{10000n}\times 10000 as a single fraction.

$$Q\times 10000n=\frac{S\left(10000-n-10000en+10000Rn\right)\times 10000}{10000n}n$$

Cancel out 10000 in both numerator and denominator.

$$Q\times 10000n=\frac{S\left(10000Rn-10000en-n+10000\right)}{n}n$$

Express \frac{S\left(10000Rn-10000en-n+10000\right)}{n}n as a single fraction.

$$Q\times 10000n=\frac{S\left(10000Rn-10000en-n+10000\right)n}{n}$$

Cancel out n in both numerator and denominator.

$$Q\times 10000n=S\left(10000Rn-10000en-n+10000\right)$$

Use the distributive property to multiply S by 10000Rn-10000en-n+10000.

$$Q\times 10000n=10000SRn-10000Sen-Sn+10000S$$

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

$$10000SRn-10000Sen-Sn+10000S=Q\times 10000n$$

Add 10000Sen to both sides.

$$10000SRn-Sn+10000S=Q\times 10000n+10000Sen$$

Add Sn to both sides.

$$10000SRn+10000S=Q\times 10000n+10000Sen+Sn$$

Subtract 10000S from both sides.

$$10000SRn=Q\times 10000n+10000Sen+Sn-10000S$$

The equation is in standard form.

$$10000SnR=Sn+10000eSn+10000Qn-10000S$$

Divide both sides by 10000Sn.

$$\frac{10000SnR}{10000Sn}=\frac{Sn+10000eSn+10000Qn-10000S}{10000Sn}$$

Dividing by 10000Sn undoes the multiplication by 10000Sn.

$$R=\frac{Sn+10000eSn+10000Qn-10000S}{10000Sn}$$

Divide 10000Qn+10000Sen+Sn-10000S by 10000Sn.

$$R=\frac{Q}{S}+e+\frac{1}{10000}-\frac{1}{n}$$

Solve for Q

$$Q=RS-eS-\frac{S}{10000}+\frac{S}{n}$$

$$n\neq 0$$