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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-18i^2-12i+12i+8)=0

We get rid of parentheses

-18i^2-12i+12i+8=0

We add all the numbers together, and all the variables

-18i^2+8=0

a = -18; b = 0; c = +8;
Δ = b2-4ac
Δ = 02-4·(-18)·8
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*-18}=\frac{-24}{-36}
=2/3
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24}{2*-18}=\frac{24}{-36}
=-2/3
$