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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

-((+56i^2+40i-56i-40))=0


We calculate terms in parentheses: -((+56i^2+40i-56i-40)), so:

(+56i^2+40i-56i-40)

We get rid of parentheses

56i^2+40i-56i-40

We add all the numbers together, and all the variables

56i^2-16i-40

Back to the equation:

-(56i^2-16i-40)


We get rid of parentheses

-56i^2+16i+40=0

a = -56; b = 16; c = +40;
Δ = b2-4ac
Δ = 162-4·(-56)·40
Δ = 9216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9216}=96$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-96}{2*-56}=\frac{-112}{-112}
=1
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+96}{2*-56}=\frac{80}{-112}
=-5/7
$