(6-3i)*(5+9i)=0

Solution for (6-3i)*(5+9i)=0 equation:

(6-3i)(5+9i)=0

We add all the numbers together, and all the variables

(-3i+6)(9i+5)=0

We multiply parentheses ..

(-27i^2-15i+54i+30)=0

We get rid of parentheses

-27i^2-15i+54i+30=0

We add all the numbers together, and all the variables

-27i^2+39i+30=0

a = -27; b = 39; c = +30;
Δ = b2-4ac
Δ = 392-4·(-27)·30
Δ = 4761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4761}=69$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-69}{2*-27}=\frac{-108}{-54}
=+2
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+69}{2*-27}=\frac{30}{-54}
=-5/9
$