(3+9i)(-9+i)=0

Solution for (3+9i)(-9+i)=0 equation:

(3+9i)(-9+i)=0

We add all the numbers together, and all the variables

(9i+3)(i-9)=0

We multiply parentheses ..

(+9i^2-81i+3i-27)=0

We get rid of parentheses

9i^2-81i+3i-27=0

We add all the numbers together, and all the variables

9i^2-78i-27=0

a = 9; b = -78; c = -27;
Δ = b2-4ac
Δ = -782-4·9·(-27)
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-84}{2*9}=\frac{-6}{18}
=-1/3
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+84}{2*9}=\frac{162}{18}
=9
$