(6+7i)(-5-2i)=

Solution for (6+7i)(-5-2i)= equation:

(6+7i)(-5-2i)=

We move all terms to the left:

(6+7i)(-5-2i)-()=0

We add all the numbers together, and all the variables

(7i+6)(-2i-5)-()=0

We add all the numbers together, and all the variables

(7i+6)(-2i-5)=0

We multiply parentheses ..

(-14i^2-35i-12i-30)=0

We get rid of parentheses

-14i^2-35i-12i-30=0

We add all the numbers together, and all the variables

-14i^2-47i-30=0

a = -14; b = -47; c = -30;
Δ = b2-4ac
Δ = -472-4·(-14)·(-30)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-23}{2*-14}=\frac{24}{-28}
=-6/7
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+23}{2*-14}=\frac{70}{-28}
=-2+1/2
$