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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+10i^2+35i+6i+21)=0

We get rid of parentheses

10i^2+35i+6i+21=0

We add all the numbers together, and all the variables

10i^2+41i+21=0

a = 10; b = 41; c = +21;
Δ = b2-4ac
Δ = 412-4·10·21
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*10}=\frac{-70}{20}
=-3+1/2
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+29}{2*10}=\frac{-12}{20}
=-3/5
$