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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-21i^2+15i-14i+10)=0

We get rid of parentheses

-21i^2+15i-14i+10=0

We add all the numbers together, and all the variables

-21i^2+i+10=0

a = -21; b = 1; c = +10;
Δ = b2-4ac
Δ = 12-4·(-21)·10
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{-(1)-29}{2*-21}=\frac{-30}{-42}
=5/7
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+29}{2*-21}=\frac{28}{-42}
=-2/3
$