Solve (6+5pi)(a+6pi)=38-9i

$$( 6 + 5 \pi ) ( a + 6 \pi ) = 38 - 9 i$$

Solve for a

$$a=-\frac{-38+9i+30\pi ^{2}+36\pi }{5\pi +6}\approx -17.099046234-0.4145944i$$

Steps for Solving Linear Equation

Apply the distributive property by multiplying each term of 6+5\pi by each term of a+6\pi .

$$6a+36\pi +5\pi a+30\pi ^{2}=38-9i$$

Subtract 36\pi from both sides.

$$6a+5\pi a+30\pi ^{2}=38-9i-36\pi$$

Subtract 30\pi ^{2} from both sides.

$$6a+5\pi a=38-9i-36\pi -30\pi ^{2}$$

Combine all terms containing a.

$$\left(6+5\pi \right)a=38-9i-36\pi -30\pi ^{2}$$

The equation is in standard form.

$$\left(5\pi +6\right)a=38-9i-30\pi ^{2}-36\pi$$

Divide both sides by 6+5\pi .

$$\frac{\left(5\pi +6\right)a}{5\pi +6}=\frac{38-9i-30\pi ^{2}-36\pi }{5\pi +6}$$

Dividing by 6+5\pi undoes the multiplication by 6+5\pi .

$$a=\frac{38-9i-30\pi ^{2}-36\pi }{5\pi +6}$$