(4+6i)(9-2i)=0

Solution for (4+6i)(9-2i)=0 equation:

(4+6i)(9-2i)=0

We add all the numbers together, and all the variables

(6i+4)(-2i+9)=0

We multiply parentheses ..

(-12i^2+54i-8i+36)=0

We get rid of parentheses

-12i^2+54i-8i+36=0

We add all the numbers together, and all the variables

-12i^2+46i+36=0

a = -12; b = 46; c = +36;
Δ = b2-4ac
Δ = 462-4·(-12)·36
Δ = 3844
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3844}=62$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-62}{2*-12}=\frac{-108}{-24}
=4+1/2
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+62}{2*-12}=\frac{16}{-24}
=-2/3
$