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

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

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

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

Combine like terms: 20i + 4i = 24i
(10 + 24i + 8i2) = 0

Solving
10 + 24i + 8i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 12i + 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}