(2-i)(5+6i)=0

Solution for (2-i)(5+6i)=0 equation:

(2-i)(5+6i)=0

We add all the numbers together, and all the variables

(-1i+2)(6i+5)=0

We multiply parentheses ..

(-6i^2-5i+12i+10)=0

We get rid of parentheses

-6i^2-5i+12i+10=0

We add all the numbers together, and all the variables

-6i^2+7i+10=0

a = -6; b = 7; c = +10;
Δ = b2-4ac
Δ = 72-4·(-6)·10
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-17}{2*-6}=\frac{-24}{-12}
=+2
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+17}{2*-6}=\frac{10}{-12}
=-5/6
$