(6-8i)(4+7i)=0

Solution for (6-8i)(4+7i)=0 equation:

(6-8i)(4+7i)=0

We add all the numbers together, and all the variables

(-8i+6)(7i+4)=0

We multiply parentheses ..

(-56i^2-32i+42i+24)=0

We get rid of parentheses

-56i^2-32i+42i+24=0

We add all the numbers together, and all the variables

-56i^2+10i+24=0

a = -56; b = 10; c = +24;
Δ = b2-4ac
Δ = 102-4·(-56)·24
Δ = 5476
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5476}=74$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-74}{2*-56}=\frac{-84}{-112}
=3/4
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+74}{2*-56}=\frac{64}{-112}
=-4/7
$