Solve gamma=a(1-s_{n}θ)

$$\gamma = a ( 1 - s _ { n } \theta )$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{\gamma }{s_{n}\theta -1}\text{, }&\theta =0\text{ or }s_{n}\neq \frac{1}{\theta }\\a\in \mathrm{C}\text{, }&\gamma =0\text{ and }s_{n}=\frac{1}{\theta }\text{ and }\theta \neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a by 1-s_{n}\theta .

$$\gamma =a-as_{n}\theta$$

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

$$a-as_{n}\theta =\gamma$$

Combine all terms containing a.

$$\left(1-s_{n}\theta \right)a=\gamma$$

Divide both sides by 1-s_{n}\theta .

$$\frac{\left(1-s_{n}\theta \right)a}{1-s_{n}\theta }=\frac{\gamma }{1-s_{n}\theta }$$

Dividing by 1-s_{n}\theta undoes the multiplication by 1-s_{n}\theta .

$$a=\frac{\gamma }{1-s_{n}\theta }$$

Solve for s_n (complex solution)

$$\left\{\begin{matrix}s_{n}=\frac{a-\gamma }{a\theta }\text{, }&a\neq 0\text{ and }\theta \neq 0\\s_{n}\in \mathrm{C}\text{, }&\left(\gamma =0\text{ and }a=0\right)\text{ or }\left(a=\gamma \text{ and }\theta =0\text{ and }\gamma \neq 0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a by 1-s_{n}\theta .

$$\gamma =a-as_{n}\theta$$

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

$$a-as_{n}\theta =\gamma$$

Subtract a from both sides.

$$-as_{n}\theta =\gamma -a$$

The equation is in standard form.

$$\left(-a\theta \right)s_{n}=\gamma -a$$

Divide both sides by -a\theta .

$$\frac{\left(-a\theta \right)s_{n}}{-a\theta }=\frac{\gamma -a}{-a\theta }$$

Dividing by -a\theta undoes the multiplication by -a\theta .

$$s_{n}=\frac{\gamma -a}{-a\theta }$$

Divide \gamma -a by -a\theta .

$$s_{n}=-\frac{\gamma -a}{a\theta }$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{\gamma }{s_{n}\theta -1}\text{, }&\theta =0\text{ or }s_{n}\neq \frac{1}{\theta }\\a\in \mathrm{R}\text{, }&\gamma =0\text{ and }s_{n}=\frac{1}{\theta }\text{ and }\theta \neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a by 1-s_{n}\theta .

$$\gamma =a-as_{n}\theta$$

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

$$a-as_{n}\theta =\gamma$$

Combine all terms containing a.

$$\left(1-s_{n}\theta \right)a=\gamma$$

Divide both sides by 1-s_{n}\theta .

$$\frac{\left(1-s_{n}\theta \right)a}{1-s_{n}\theta }=\frac{\gamma }{1-s_{n}\theta }$$

Dividing by 1-s_{n}\theta undoes the multiplication by 1-s_{n}\theta .

$$a=\frac{\gamma }{1-s_{n}\theta }$$

Solve for s_n

$$\left\{\begin{matrix}s_{n}=\frac{a-\gamma }{a\theta }\text{, }&a\neq 0\text{ and }\theta \neq 0\\s_{n}\in \mathrm{R}\text{, }&\left(\gamma =0\text{ and }a=0\right)\text{ or }\left(a=\gamma \text{ and }\theta =0\text{ and }\gamma \neq 0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a by 1-s_{n}\theta .

$$\gamma =a-as_{n}\theta$$

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

$$a-as_{n}\theta =\gamma$$

Subtract a from both sides.

$$-as_{n}\theta =\gamma -a$$

The equation is in standard form.

$$\left(-a\theta \right)s_{n}=\gamma -a$$

Divide both sides by -a\theta .

$$\frac{\left(-a\theta \right)s_{n}}{-a\theta }=\frac{\gamma -a}{-a\theta }$$

Dividing by -a\theta undoes the multiplication by -a\theta .

$$s_{n}=\frac{\gamma -a}{-a\theta }$$

Divide \gamma -a by -a\theta .

$$s_{n}=-\frac{\gamma -a}{a\theta }$$