=(3-2j)(2+8j)

Solution for =(3-2j)(2+8j) equation:

Simplifying
0 = (3 + -2j)(2 + 8j)

Multiply (3 + -2j) * (2 + 8j)
0 = (3(2 + 8j) + -2j * (2 + 8j))
0 = ((2 * 3 + 8j * 3) + -2j * (2 + 8j))
0 = ((6 + 24j) + -2j * (2 + 8j))
0 = (6 + 24j + (2 * -2j + 8j * -2j))
0 = (6 + 24j + (-4j + -16j2))

Combine like terms: 24j + -4j = 20j
0 = (6 + 20j + -16j2)

Solving
0 = 6 + 20j + -16j2

Solving for variable 'j'.

Combine like terms: 0 + -6 = -6
-6 + -20j + 16j2 = 6 + 20j + -16j2 + -6 + -20j + 16j2

Reorder the terms:
-6 + -20j + 16j2 = 6 + -6 + 20j + -20j + -16j2 + 16j2

Combine like terms: 6 + -6 = 0
-6 + -20j + 16j2 = 0 + 20j + -20j + -16j2 + 16j2
-6 + -20j + 16j2 = 20j + -20j + -16j2 + 16j2

Combine like terms: 20j + -20j = 0
-6 + -20j + 16j2 = 0 + -16j2 + 16j2
-6 + -20j + 16j2 = -16j2 + 16j2

Combine like terms: -16j2 + 16j2 = 0
-6 + -20j + 16j2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -10j + 8j2) = 0

Factor a trinomial.
2((-1 + -4j)(3 + -2j)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + -4j)' equal to zero and attempt to solve:

Simplifying
-1 + -4j = 0

Solving
-1 + -4j = 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 + -4j = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4j = 0 + 1
-4j = 0 + 1

Combine like terms: 0 + 1 = 1
-4j = 1

Divide each side by '-4'.
j = -0.25

Simplifying
j = -0.25
Subproblem 2
Set the factor '(3 + -2j)' equal to zero and attempt to solve:

Simplifying
3 + -2j = 0

Solving
3 + -2j = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2j = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2j = 0 + -3
-2j = 0 + -3

Combine like terms: 0 + -3 = -3
-2j = -3

Divide each side by '-2'.
j = 1.5

Simplifying
j = 1.5
Solution
j = {-0.25, 1.5}