(-3-9i)(1+10i)=0

Solution for (-3-9i)(1+10i)=0 equation:

(-3-9i)(1+10i)=0

We add all the numbers together, and all the variables

(-9i-3)(10i+1)=0

We multiply parentheses ..

(-90i^2-9i-30i-3)=0

We get rid of parentheses

-90i^2-9i-30i-3=0

We add all the numbers together, and all the variables

-90i^2-39i-3=0

a = -90; b = -39; c = -3;
Δ = b2-4ac
Δ = -392-4·(-90)·(-3)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-21}{2*-90}=\frac{18}{-180}
=-1/10
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+21}{2*-90}=\frac{60}{-180}
=-1/3
$