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

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

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

We add all the numbers together, and all the variables

(-1i+4)(6i-2)=0

We multiply parentheses ..

(-6i^2+2i+24i-8)=0

We get rid of parentheses

-6i^2+2i+24i-8=0

We add all the numbers together, and all the variables

-6i^2+26i-8=0

a = -6; b = 26; c = -8;
Δ = b2-4ac
Δ = 262-4·(-6)·(-8)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-22}{2*-6}=\frac{-48}{-12}
=+4
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+22}{2*-6}=\frac{-4}{-12}
=1/3
$