(3+3j)(9-2j)=

Solution for (3+3j)(9-2j)= equation:

Simplifying
(3 + 3j)(9 + -2j) = 0

Multiply (3 + 3j) * (9 + -2j)
(3(9 + -2j) + 3j * (9 + -2j)) = 0
((9 * 3 + -2j * 3) + 3j * (9 + -2j)) = 0
((27 + -6j) + 3j * (9 + -2j)) = 0
(27 + -6j + (9 * 3j + -2j * 3j)) = 0
(27 + -6j + (27j + -6j2)) = 0

Combine like terms: -6j + 27j = 21j
(27 + 21j + -6j2) = 0

Solving
27 + 21j + -6j2 = 0

Solving for variable 'j'.

Factor out the Greatest Common Factor (GCF), '3'.
3(9 + 7j + -2j2) = 0

Factor a trinomial.
3((9 + -2j)(1 + j)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(9 + -2j)' equal to zero and attempt to solve:

Simplifying
9 + -2j = 0

Solving
9 + -2j = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2j = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2j = 0 + -9
-2j = 0 + -9

Combine like terms: 0 + -9 = -9
-2j = -9

Divide each side by '-2'.
j = 4.5

Simplifying
j = 4.5
Subproblem 2
Set the factor '(1 + j)' equal to zero and attempt to solve:

Simplifying
1 + j = 0

Solving
1 + j = 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 + j = 0 + -1

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

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

Simplifying
j = -1
Solution
j = {4.5, -1}