(2+4i)(3-5i)=

Solution for (2+4i)(3-5i)= equation:

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

Multiply (2 + 4i) * (3 + -5i)
(2(3 + -5i) + 4i * (3 + -5i)) = 0
((3 * 2 + -5i * 2) + 4i * (3 + -5i)) = 0
((6 + -10i) + 4i * (3 + -5i)) = 0
(6 + -10i + (3 * 4i + -5i * 4i)) = 0
(6 + -10i + (12i + -20i2)) = 0

Combine like terms: -10i + 12i = 2i
(6 + 2i + -20i2) = 0

Solving
6 + 2i + -20i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + i + -10i2) = 0

Factor a trinomial.
2((3 + -5i)(1 + 2i)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -5i)' equal to zero and attempt to solve:

Simplifying
3 + -5i = 0

Solving
3 + -5i = 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 + -5i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5i = 0 + -3
-5i = 0 + -3

Combine like terms: 0 + -3 = -3
-5i = -3

Divide each side by '-5'.
i = 0.6

Simplifying
i = 0.6
Subproblem 2
Set the factor '(1 + 2i)' equal to zero and attempt to solve:

Simplifying
1 + 2i = 0

Solving
1 + 2i = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2i = 0 + -1
2i = 0 + -1

Combine like terms: 0 + -1 = -1
2i = -1

Divide each side by '2'.
i = -0.5

Simplifying
i = -0.5
Solution
i = {0.6, -0.5}