4(3-j)+2j(j-3)+8(j-3)=0

Solution for 4(3-j)+2j(j-3)+8(j-3)=0 equation:

Simplifying
4(3 + -1j) + 2j(j + -3) + 8(j + -3) = 0
(3 * 4 + -1j * 4) + 2j(j + -3) + 8(j + -3) = 0
(12 + -4j) + 2j(j + -3) + 8(j + -3) = 0

Reorder the terms:
12 + -4j + 2j(-3 + j) + 8(j + -3) = 0
12 + -4j + (-3 * 2j + j * 2j) + 8(j + -3) = 0
12 + -4j + (-6j + 2j2) + 8(j + -3) = 0

Reorder the terms:
12 + -4j + -6j + 2j2 + 8(-3 + j) = 0
12 + -4j + -6j + 2j2 + (-3 * 8 + j * 8) = 0
12 + -4j + -6j + 2j2 + (-24 + 8j) = 0

Reorder the terms:
12 + -24 + -4j + -6j + 8j + 2j2 = 0

Combine like terms: 12 + -24 = -12
-12 + -4j + -6j + 8j + 2j2 = 0

Combine like terms: -4j + -6j = -10j
-12 + -10j + 8j + 2j2 = 0

Combine like terms: -10j + 8j = -2j
-12 + -2j + 2j2 = 0

Solving
-12 + -2j + 2j2 = 0

Solving for variable 'j'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -1j + j2) = 0

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

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

Simplifying
-2 + -1j = 0

Solving
-2 + -1j = 0

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

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

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

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

Divide each side by '-1'.
j = -2

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

Simplifying
3 + -1j = 0

Solving
3 + -1j = 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 + -1j = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1j = 0 + -3
-1j = 0 + -3

Combine like terms: 0 + -3 = -3
-1j = -3

Divide each side by '-1'.
j = 3

Simplifying
j = 3
Solution
j = {-2, 3}