(4+8i)(3-7i)=0

Solution for (4+8i)(3-7i)=0 equation:

(4+8i)(3-7i)=0

We add all the numbers together, and all the variables

(8i+4)(-7i+3)=0

We multiply parentheses ..

(-56i^2+24i-28i+12)=0

We get rid of parentheses

-56i^2+24i-28i+12=0

We add all the numbers together, and all the variables

-56i^2-4i+12=0

a = -56; b = -4; c = +12;
Δ = b2-4ac
Δ = -42-4·(-56)·12
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-52}{2*-56}=\frac{-48}{-112}
=3/7
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+52}{2*-56}=\frac{56}{-112}
=-1/2
$