(2-5I)(3-4I)=0

Solution for (2-5I)(3-4I)=0 equation:

Simplifying
(2 + -5I)(3 + -4I) = 0

Multiply (2 + -5I) * (3 + -4I)
(2(3 + -4I) + -5I * (3 + -4I)) = 0
((3 * 2 + -4I * 2) + -5I * (3 + -4I)) = 0
((6 + -8I) + -5I * (3 + -4I)) = 0
(6 + -8I + (3 * -5I + -4I * -5I)) = 0
(6 + -8I + (-15I + 20I2)) = 0

Combine like terms: -8I + -15I = -23I
(6 + -23I + 20I2) = 0

Solving
6 + -23I + 20I2 = 0

Solving for variable 'I'.

Factor a trinomial.
(2 + -5I)(3 + -4I) = 0

Subproblem 1
Set the factor '(2 + -5I)' equal to zero and attempt to solve:

Simplifying
2 + -5I = 0

Solving
2 + -5I = 0

Move all terms containing I to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -5I = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5I = 0 + -2
-5I = 0 + -2

Combine like terms: 0 + -2 = -2
-5I = -2

Divide each side by '-5'.
I = 0.4

Simplifying
I = 0.4
Subproblem 2
Set the factor '(3 + -4I)' equal to zero and attempt to solve:

Simplifying
3 + -4I = 0

Solving
3 + -4I = 0

Move all terms containing I to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -4I = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4I = 0 + -3
-4I = 0 + -3

Combine like terms: 0 + -3 = -3
-4I = -3

Divide each side by '-4'.
I = 0.75

Simplifying
I = 0.75
Solution
I = {0.4, 0.75}