(2+i)(3-7i)=0

Solution for (2+i)(3-7i)=0 equation:

(2+i)(3-7i)=0

We add all the numbers together, and all the variables

(i+2)(-7i+3)=0

We multiply parentheses ..

(-7i^2+3i-14i+6)=0

We get rid of parentheses

-7i^2+3i-14i+6=0

We add all the numbers together, and all the variables

-7i^2-11i+6=0

a = -7; b = -11; c = +6;
Δ = b2-4ac
Δ = -112-4·(-7)·6
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{-(-11)-17}{2*-7}=\frac{-6}{-14}
=3/7
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+17}{2*-7}=\frac{28}{-14}
=-2
$