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

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

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

Multiply (3 + 6j) * (5 + -1j)
(3(5 + -1j) + 6j * (5 + -1j)) = 0
((5 * 3 + -1j * 3) + 6j * (5 + -1j)) = 0
((15 + -3j) + 6j * (5 + -1j)) = 0
(15 + -3j + (5 * 6j + -1j * 6j)) = 0
(15 + -3j + (30j + -6j2)) = 0

Combine like terms: -3j + 30j = 27j
(15 + 27j + -6j2) = 0

Solving
15 + 27j + -6j2 = 0

Solving for variable 'j'.

Factor out the Greatest Common Factor (GCF), '3'.
3(5 + 9j + -2j2) = 0

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

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

Simplifying
5 + -1j = 0

Solving
5 + -1j = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1j = 0 + -5

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

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

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

Simplifying
j = 5
Subproblem 2
Set the factor '(1 + 2j)' equal to zero and attempt to solve:

Simplifying
1 + 2j = 0

Solving
1 + 2j = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2j = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2j = 0 + -1
2j = 0 + -1

Combine like terms: 0 + -1 = -1
2j = -1

Divide each side by '2'.
j = -0.5

Simplifying
j = -0.5
Solution
j = {5, -0.5}