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

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

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

Multiply (2 + 4i) * (5 + -2i)
(2(5 + -2i) + 4i * (5 + -2i)) = 0
((5 * 2 + -2i * 2) + 4i * (5 + -2i)) = 0
((10 + -4i) + 4i * (5 + -2i)) = 0
(10 + -4i + (5 * 4i + -2i * 4i)) = 0
(10 + -4i + (20i + -8i2)) = 0

Combine like terms: -4i + 20i = 16i
(10 + 16i + -8i2) = 0

Solving
10 + 16i + -8i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 8i + -4i2) = 0

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

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

Simplifying
5 + -2i = 0

Solving
5 + -2i = 0

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

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

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

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

Divide each side by '-2'.
i = 2.5

Simplifying
i = 2.5
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 = {2.5, -0.5}