(-5-2i)(3+7i)=0

Solution for (-5-2i)(3+7i)=0 equation:

(-5-2i)(3+7i)=0

We add all the numbers together, and all the variables

(-2i-5)(7i+3)=0

We multiply parentheses ..

(-14i^2-6i-35i-15)=0

We get rid of parentheses

-14i^2-6i-35i-15=0

We add all the numbers together, and all the variables

-14i^2-41i-15=0

a = -14; b = -41; c = -15;
Δ = b2-4ac
Δ = -412-4·(-14)·(-15)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-41)-29}{2*-14}=\frac{12}{-28}
=-3/7
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+29}{2*-14}=\frac{70}{-28}
=-2+1/2
$