(7-8i)(5+6i)=0

Solution for (7-8i)(5+6i)=0 equation:

(7-8i)(5+6i)=0

We add all the numbers together, and all the variables

(-8i+7)(6i+5)=0

We multiply parentheses ..

(-48i^2-40i+42i+35)=0

We get rid of parentheses

-48i^2-40i+42i+35=0

We add all the numbers together, and all the variables

-48i^2+2i+35=0

a = -48; b = 2; c = +35;
Δ = b2-4ac
Δ = 22-4·(-48)·35
Δ = 6724
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6724}=82$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-82}{2*-48}=\frac{-84}{-96}
=7/8
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+82}{2*-48}=\frac{80}{-96}
=-5/6
$