(9+3i)*(2-10i)=0

Solution for (9+3i)*(2-10i)=0 equation:

(9+3i)(2-10i)=0

We add all the numbers together, and all the variables

(3i+9)(-10i+2)=0

We multiply parentheses ..

(-30i^2+6i-90i+18)=0

We get rid of parentheses

-30i^2+6i-90i+18=0

We add all the numbers together, and all the variables

-30i^2-84i+18=0

a = -30; b = -84; c = +18;
Δ = b2-4ac
Δ = -842-4·(-30)·18
Δ = 9216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9216}=96$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-96}{2*-30}=\frac{-12}{-60}
=1/5
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+96}{2*-30}=\frac{180}{-60}
=-3
$