(5+2i)(1+3i)=0

Solution for (5+2i)(1+3i)=0 equation:

(5+2i)(1+3i)=0

We add all the numbers together, and all the variables

(2i+5)(3i+1)=0

We multiply parentheses ..

(+6i^2+2i+15i+5)=0

We get rid of parentheses

6i^2+2i+15i+5=0

We add all the numbers together, and all the variables

6i^2+17i+5=0

a = 6; b = 17; c = +5;
Δ = b2-4ac
Δ = 172-4·6·5
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-13}{2*6}=\frac{-30}{12}
=-2+1/2
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+13}{2*6}=\frac{-4}{12}
=-1/3
$