(7-2i)(3+5i)=0

Solution for (7-2i)(3+5i)=0 equation:

(7-2i)(3+5i)=0

We add all the numbers together, and all the variables

(-2i+7)(5i+3)=0

We multiply parentheses ..

(-10i^2-6i+35i+21)=0

We get rid of parentheses

-10i^2-6i+35i+21=0

We add all the numbers together, and all the variables

-10i^2+29i+21=0

a = -10; b = 29; c = +21;
Δ = b2-4ac
Δ = 292-4·(-10)·21
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-41}{2*-10}=\frac{-70}{-20}
=3+1/2
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+41}{2*-10}=\frac{12}{-20}
=-3/5
$