(-1+5i)(-2-3i)=0

Solution for (-1+5i)(-2-3i)=0 equation:

(-1+5i)(-2-3i)=0

We add all the numbers together, and all the variables

(5i-1)(-3i-2)=0

We multiply parentheses ..

(-15i^2-10i+3i+2)=0

We get rid of parentheses

-15i^2-10i+3i+2=0

We add all the numbers together, and all the variables

-15i^2-7i+2=0

a = -15; b = -7; c = +2;
Δ = b2-4ac
Δ = -72-4·(-15)·2
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-13}{2*-15}=\frac{-6}{-30}
=1/5
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+13}{2*-15}=\frac{20}{-30}
=-2/3
$