(4+12i)(6-12i)=0

Solution for (4+12i)(6-12i)=0 equation:

(4+12i)(6-12i)=0

We add all the numbers together, and all the variables

(12i+4)(-12i+6)=0

We multiply parentheses ..

(-144i^2+72i-48i+24)=0

We get rid of parentheses

-144i^2+72i-48i+24=0

We add all the numbers together, and all the variables

-144i^2+24i+24=0

a = -144; b = 24; c = +24;
Δ = b2-4ac
Δ = 242-4·(-144)·24
Δ = 14400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14400}=120$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-120}{2*-144}=\frac{-144}{-288}
=1/2
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+120}{2*-144}=\frac{96}{-288}
=-1/3
$