2(2-j)=4(j+10)j

Solution for 2(2-j)=4(j+10)j equation:

Simplifying
2(2 + -1j) = 4(j + 10) * j
(2 * 2 + -1j * 2) = 4(j + 10) * j
(4 + -2j) = 4(j + 10) * j

Reorder the terms:
4 + -2j = 4(10 + j) * j

Reorder the terms for easier multiplication:
4 + -2j = 4j(10 + j)
4 + -2j = (10 * 4j + j * 4j)
4 + -2j = (40j + 4j2)

Solving
4 + -2j = 40j + 4j2

Solving for variable 'j'.

Combine like terms: -2j + -40j = -42j
4 + -42j + -4j2 = 40j + 4j2 + -40j + -4j2

Reorder the terms:
4 + -42j + -4j2 = 40j + -40j + 4j2 + -4j2

Combine like terms: 40j + -40j = 0
4 + -42j + -4j2 = 0 + 4j2 + -4j2
4 + -42j + -4j2 = 4j2 + -4j2

Combine like terms: 4j2 + -4j2 = 0
4 + -42j + -4j2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + -21j + -2j2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(2 + -21j + -2j2)' equal to zero and attempt to solve:

Simplifying
2 + -21j + -2j2 = 0

Solving
2 + -21j + -2j2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-1 + 10.5j + j2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 10.5j + 1 + j2 = 0 + 1

Reorder the terms:
-1 + 1 + 10.5j + j2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 10.5j + j2 = 0 + 1
10.5j + j2 = 0 + 1

Combine like terms: 0 + 1 = 1
10.5j + j2 = 1

The j term is 10.5j.  Take half its coefficient (5.25).
Square it (27.5625) and add it to both sides.

Add '27.5625' to each side of the equation.
10.5j + 27.5625 + j2 = 1 + 27.5625

Reorder the terms:
27.5625 + 10.5j + j2 = 1 + 27.5625

Combine like terms: 1 + 27.5625 = 28.5625
27.5625 + 10.5j + j2 = 28.5625

Factor a perfect square on the left side:
(j + 5.25)(j + 5.25) = 28.5625

Calculate the square root of the right side: 5.344389582

Break this problem into two subproblems by setting 
(j + 5.25) equal to 5.344389582 and -5.344389582.

Subproblem 1
j + 5.25 = 5.344389582

Simplifying
j + 5.25 = 5.344389582

Reorder the terms:
5.25 + j = 5.344389582

Solving
5.25 + j = 5.344389582

Solving for variable 'j'.

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

Add '-5.25' to each side of the equation.
5.25 + -5.25 + j = 5.344389582 + -5.25

Combine like terms: 5.25 + -5.25 = 0.00
0.00 + j = 5.344389582 + -5.25
j = 5.344389582 + -5.25

Combine like terms: 5.344389582 + -5.25 = 0.094389582
j = 0.094389582

Simplifying
j = 0.094389582

Subproblem 2
j + 5.25 = -5.344389582

Simplifying
j + 5.25 = -5.344389582

Reorder the terms:
5.25 + j = -5.344389582

Solving
5.25 + j = -5.344389582

Solving for variable 'j'.

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

Add '-5.25' to each side of the equation.
5.25 + -5.25 + j = -5.344389582 + -5.25

Combine like terms: 5.25 + -5.25 = 0.00
0.00 + j = -5.344389582 + -5.25
j = -5.344389582 + -5.25

Combine like terms: -5.344389582 + -5.25 = -10.594389582
j = -10.594389582

Simplifying
j = -10.594389582

Solution
The solution to the problem is based on the solutions
from the subproblems.
j = {0.094389582, -10.594389582}
Solution
j = {0.094389582, -10.594389582}