(3+6I)(5-I)=

Solution for (3+6I)(5-I)= equation:

Simplifying
(3 + 6I)(5 + -1I) = 0

Multiply (3 + 6I) * (5 + -1I)
(3(5 + -1I) + 6I * (5 + -1I)) = 0
((5 * 3 + -1I * 3) + 6I * (5 + -1I)) = 0
((15 + -3I) + 6I * (5 + -1I)) = 0
(15 + -3I + (5 * 6I + -1I * 6I)) = 0
(15 + -3I + (30I + -6I2)) = 0

Combine like terms: -3I + 30I = 27I
(15 + 27I + -6I2) = 0

Solving
15 + 27I + -6I2 = 0

Solving for variable 'I'.

Factor out the Greatest Common Factor (GCF), '3'.
3(5 + 9I + -2I2) = 0

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

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

Simplifying
5 + -1I = 0

Solving
5 + -1I = 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 + -1I = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1I = 0 + -5
-1I = 0 + -5

Combine like terms: 0 + -5 = -5
-1I = -5

Divide each side by '-1'.
I = 5

Simplifying
I = 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 = {5, -0.5}