(2-5i)(3+10i)=0

Solution for (2-5i)(3+10i)=0 equation:

(2-5i)(3+10i)=0

We add all the numbers together, and all the variables

(-5i+2)(10i+3)=0

We multiply parentheses ..

(-50i^2-15i+20i+6)=0

We get rid of parentheses

-50i^2-15i+20i+6=0

We add all the numbers together, and all the variables

-50i^2+5i+6=0

a = -50; b = 5; c = +6;
Δ = b2-4ac
Δ = 52-4·(-50)·6
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-35}{2*-50}=\frac{-40}{-100}
=2/5
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+35}{2*-50}=\frac{30}{-100}
=-3/10
$