(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 + -1i + -10i2) = 0

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

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
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
Solution
i = {0.5, -0.6}