(8+4i)(9-3i)=0

Solution for (8+4i)(9-3i)=0 equation:

(8+4i)(9-3i)=0

We add all the numbers together, and all the variables

(4i+8)(-3i+9)=0

We multiply parentheses ..

(-12i^2+36i-24i+72)=0

We get rid of parentheses

-12i^2+36i-24i+72=0

We add all the numbers together, and all the variables

-12i^2+12i+72=0

a = -12; b = 12; c = +72;
Δ = b2-4ac
Δ = 122-4·(-12)·72
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-60}{2*-12}=\frac{-72}{-24}
=+3
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+60}{2*-12}=\frac{48}{-24}
=-2
$