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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -21; b = -29; c = +10;
Δ = b2-4ac
Δ = -292-4·(-21)·10
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*-21}=\frac{-12}{-42}
=2/7
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+41}{2*-21}=\frac{70}{-42}
=-1+2/3
$