(1-6i)(-5+8i)=0

Solution for (1-6i)(-5+8i)=0 equation:

(1-6i)(-5+8i)=0

We add all the numbers together, and all the variables

(-6i+1)(8i-5)=0

We multiply parentheses ..

(-48i^2+30i+8i-5)=0

We get rid of parentheses

-48i^2+30i+8i-5=0

We add all the numbers together, and all the variables

-48i^2+38i-5=0

a = -48; b = 38; c = -5;
Δ = b2-4ac
Δ = 382-4·(-48)·(-5)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-22}{2*-48}=\frac{-60}{-96}
=5/8
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+22}{2*-48}=\frac{-16}{-96}
=1/6
$