(5+3i)(8+2i)=0

Solution for (5+3i)(8+2i)=0 equation:

(5+3i)(8+2i)=0

We add all the numbers together, and all the variables

(3i+5)(2i+8)=0

We multiply parentheses ..

(+6i^2+24i+10i+40)=0

We get rid of parentheses

6i^2+24i+10i+40=0

We add all the numbers together, and all the variables

6i^2+34i+40=0

a = 6; b = 34; c = +40;
Δ = b2-4ac
Δ = 342-4·6·40
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-14}{2*6}=\frac{-48}{12}
=-4
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+14}{2*6}=\frac{-20}{12}
=-1+2/3
$