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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-14i^2+35i-6i+15)=0

We get rid of parentheses

-14i^2+35i-6i+15=0

We add all the numbers together, and all the variables

-14i^2+29i+15=0

a = -14; b = 29; c = +15;
Δ = b2-4ac
Δ = 292-4·(-14)·15
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*-14}=\frac{-70}{-28}
=2+1/2
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+41}{2*-14}=\frac{12}{-28}
=-3/7
$