Solve (12+a):(6a-8)=3i2

$$( 12 + a ) : ( 6 a - 8 ) = 3 i 2$$

Solve for a

$$a=\frac{1716}{1297}-\frac{480}{1297}i\approx 1.3230532-0.370084811i$$

Steps for Solving Linear Equation

Variable a cannot be equal to \frac{4}{3} since division by zero is not defined. Multiply both sides of the equation by 2\left(3a-4\right).

$$12+a=3i\times 2\times 2\left(3a-4\right)$$

Multiply 3i and 2 to get 6i.

$$12+a=6i\times 2\left(3a-4\right)$$

Multiply 6i and 2 to get 12i.

$$12+a=12i\left(3a-4\right)$$

Use the distributive property to multiply 12i by 3a-4.

$$12+a=36ia-48i$$

Subtract 36ia from both sides.

$$12+a-36ia=-48i$$

Combine a and -36ia to get \left(1-36i\right)a.

$$12+\left(1-36i\right)a=-48i$$

Subtract 12 from both sides.

$$\left(1-36i\right)a=-48i-12$$

The equation is in standard form.

$$\left(1-36i\right)a=-12-48i$$

Divide both sides by 1-36i.

$$\frac{\left(1-36i\right)a}{1-36i}=\frac{-12-48i}{1-36i}$$

Dividing by 1-36i undoes the multiplication by 1-36i.

$$a=\frac{-12-48i}{1-36i}$$

Divide -12-48i by 1-36i.

$$a=\frac{1716}{1297}-\frac{480}{1297}i$$