(3i-6)(2i+4)=0

Solution for (3i-6)(2i+4)=0 equation:

(3i-6)(2i+4)=0

We multiply parentheses ..

(+6i^2+12i-12i-24)=0

We get rid of parentheses

6i^2+12i-12i-24=0

We add all the numbers together, and all the variables

6i^2-24=0

a = 6; b = 0; c = -24;
Δ = b2-4ac
Δ = 02-4·6·(-24)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24}{2*6}=\frac{-24}{12}
=-2
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24}{2*6}=\frac{24}{12}
=2
$