Solve (2-ai)(a_{n}+4)=36

$$( 2 - a i ) ( a _ { n } + 4 ) = 36$$

Solve for a

$$a=\frac{2\left(a_{n}-14\right)}{ia_{n}+4i}$$

$$a_{n}\neq -4$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2-ai by a_{n}+4.

$$\left(2-ai\right)a_{n}+4\left(2-ai\right)=36$$

Multiply -1 and i to get -i.

$$\left(2-ia\right)a_{n}+4\left(2-ai\right)=36$$

Use the distributive property to multiply 2-ia by a_{n}.

$$2a_{n}-iaa_{n}+4\left(2-ai\right)=36$$

Multiply -1 and i to get -i.

$$2a_{n}-iaa_{n}+4\left(2-ia\right)=36$$

Use the distributive property to multiply 4 by 2-ia.

$$2a_{n}-iaa_{n}+8-4ia=36$$

Subtract 2a_{n} from both sides.

$$-iaa_{n}+8-4ia=36-2a_{n}$$

Subtract 8 from both sides.

$$-iaa_{n}-4ia=36-2a_{n}-8$$

Subtract 8 from 36 to get 28.

$$-iaa_{n}-4ia=28-2a_{n}$$

Combine all terms containing a.

$$\left(-ia_{n}-4i\right)a=28-2a_{n}$$

The equation is in standard form.

$$\left(-4i-ia_{n}\right)a=28-2a_{n}$$

Divide both sides by -ia_{n}-4i.

$$\frac{\left(-4i-ia_{n}\right)a}{-4i-ia_{n}}=\frac{28-2a_{n}}{-4i-ia_{n}}$$

Dividing by -ia_{n}-4i undoes the multiplication by -ia_{n}-4i.

$$a=\frac{28-2a_{n}}{-4i-ia_{n}}$$

Divide 28-2a_{n} by -ia_{n}-4i.

$$a=-\frac{2\left(14-a_{n}\right)}{ia_{n}+4i}$$

Solve for a_n

$$a_{n}=\frac{4\left(ia+7\right)}{2-ia}$$

$$a\neq -2i$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2-ai by a_{n}+4.

$$\left(2-ai\right)a_{n}+4\left(2-ai\right)=36$$

Subtract 4\left(2-ai\right) from both sides.

$$\left(2-ai\right)a_{n}=36-4\left(2-ai\right)$$

Multiply -1 and i to get -i.

$$\left(2-ia\right)a_{n}=36-4\left(2-ai\right)$$

Use the distributive property to multiply 2-ia by a_{n}.

$$2a_{n}-iaa_{n}=36-4\left(2-ai\right)$$

Multiply -1 and i to get -i.

$$2a_{n}-iaa_{n}=36-4\left(2-ia\right)$$

Use the distributive property to multiply -4 by 2-ia.

$$2a_{n}-iaa_{n}=36-8+4ia$$

Subtract 8 from 36 to get 28.

$$2a_{n}-iaa_{n}=28+4ia$$

Combine all terms containing a_{n}.

$$\left(2-ia\right)a_{n}=28+4ia$$

The equation is in standard form.

$$\left(2-ia\right)a_{n}=4ia+28$$

Divide both sides by 2-ia.

$$\frac{\left(2-ia\right)a_{n}}{2-ia}=\frac{4ia+28}{2-ia}$$

Dividing by 2-ia undoes the multiplication by 2-ia.

$$a_{n}=\frac{4ia+28}{2-ia}$$

Divide 28+4ia by 2-ia.

$$a_{n}=\frac{4\left(ia+7\right)}{2-ia}$$