(5+2i)(3+6i)=

Solution for (5+2i)(3+6i)= equation:

Simplifying
(5 + 2i)(3 + 6i) = 0

Multiply (5 + 2i) * (3 + 6i)
(5(3 + 6i) + 2i * (3 + 6i)) = 0
((3 * 5 + 6i * 5) + 2i * (3 + 6i)) = 0
((15 + 30i) + 2i * (3 + 6i)) = 0
(15 + 30i + (3 * 2i + 6i * 2i)) = 0
(15 + 30i + (6i + 12i2)) = 0

Combine like terms: 30i + 6i = 36i
(15 + 36i + 12i2) = 0

Solving
15 + 36i + 12i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '3'.
3(5 + 12i + 4i2) = 0

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

Ignore the factor 3.
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}