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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

21i^2-29i+10=0

a = 21; b = -29; c = +10;
Δ = b2-4ac
Δ = -292-4·21·10
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-1}{2*21}=\frac{28}{42}
=2/3
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+1}{2*21}=\frac{30}{42}
=5/7
$