(5+6i)(-4+7i)=0

Solution for (5+6i)(-4+7i)=0 equation:

(5+6i)(-4+7i)=0

We add all the numbers together, and all the variables

(6i+5)(7i-4)=0

We multiply parentheses ..

(+42i^2-24i+35i-20)=0

We get rid of parentheses

42i^2-24i+35i-20=0

We add all the numbers together, and all the variables

42i^2+11i-20=0

a = 42; b = 11; c = -20;
Δ = b2-4ac
Δ = 112-4·42·(-20)
Δ = 3481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3481}=59$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-59}{2*42}=\frac{-70}{84}
=-5/6
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+59}{2*42}=\frac{48}{84}
=4/7
$