(-1+4i)(3-8i)=0

Solution for (-1+4i)(3-8i)=0 equation:

(-1+4i)(3-8i)=0

We add all the numbers together, and all the variables

(4i-1)(-8i+3)=0

We multiply parentheses ..

(-32i^2+12i+8i-3)=0

We get rid of parentheses

-32i^2+12i+8i-3=0

We add all the numbers together, and all the variables

-32i^2+20i-3=0

a = -32; b = 20; c = -3;
Δ = b2-4ac
Δ = 202-4·(-32)·(-3)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4}{2*-32}=\frac{-24}{-64}
=3/8
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4}{2*-32}=\frac{-16}{-64}
=1/4
$