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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

-18i^2-27i-10i-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{20}{-36}
=-5/9
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+17}{2*-18}=\frac{54}{-36}
=-1+1/2
$