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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-18i^2-27i+30i+45)=0

We get rid of parentheses

-18i^2-27i+30i+45=0

We add all the numbers together, and all the variables

-18i^2+3i+45=0

a = -18; b = 3; c = +45;
Δ = b2-4ac
Δ = 32-4·(-18)·45
Δ = 3249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3249}=57$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-57}{2*-18}=\frac{-60}{-36}
=1+2/3
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+57}{2*-18}=\frac{54}{-36}
=-1+1/2
$