(-3+2i)(5-9i)=0

Solution for (-3+2i)(5-9i)=0 equation:

(-3+2i)(5-9i)=0

We add all the numbers together, and all the variables

(2i-3)(-9i+5)=0

We multiply parentheses ..

(-18i^2+10i+27i-15)=0

We get rid of parentheses

-18i^2+10i+27i-15=0

We add all the numbers together, and all the variables

-18i^2+37i-15=0

a = -18; b = 37; c = -15;
Δ = b2-4ac
Δ = 372-4·(-18)·(-15)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37)-17}{2*-18}=\frac{-54}{-36}
=1+1/2
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+17}{2*-18}=\frac{-20}{-36}
=5/9
$