(5+2i)(12+6i)=0

Solution for (5+2i)(12+6i)=0 equation:

(5+2i)(12+6i)=0

We add all the numbers together, and all the variables

(2i+5)(6i+12)=0

We multiply parentheses ..

(+12i^2+24i+30i+60)=0

We get rid of parentheses

12i^2+24i+30i+60=0

We add all the numbers together, and all the variables

12i^2+54i+60=0

a = 12; b = 54; c = +60;
Δ = b2-4ac
Δ = 542-4·12·60
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-6}{2*12}=\frac{-60}{24}
=-2+1/2
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+6}{2*12}=\frac{-48}{24}
=-2
$