(6-8i)(2+7i)=0

Solution for (6-8i)(2+7i)=0 equation:

(6-8i)(2+7i)=0

We add all the numbers together, and all the variables

(-8i+6)(7i+2)=0

We multiply parentheses ..

(-56i^2-16i+42i+12)=0

We get rid of parentheses

-56i^2-16i+42i+12=0

We add all the numbers together, and all the variables

-56i^2+26i+12=0

a = -56; b = 26; c = +12;
Δ = b2-4ac
Δ = 262-4·(-56)·12
Δ = 3364
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3364}=58$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-58}{2*-56}=\frac{-84}{-112}
=3/4
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+58}{2*-56}=\frac{32}{-112}
=-2/7
$