3(5j+2)=2(3j-6)j-2

Solution for 3(5j+2)=2(3j-6)j-2 equation:

Simplifying
3(5j + 2) = 2(3j + -6) * j + -2

Reorder the terms:
3(2 + 5j) = 2(3j + -6) * j + -2
(2 * 3 + 5j * 3) = 2(3j + -6) * j + -2
(6 + 15j) = 2(3j + -6) * j + -2

Reorder the terms:
6 + 15j = 2(-6 + 3j) * j + -2

Reorder the terms for easier multiplication:
6 + 15j = 2j(-6 + 3j) + -2
6 + 15j = (-6 * 2j + 3j * 2j) + -2
6 + 15j = (-12j + 6j2) + -2

Reorder the terms:
6 + 15j = -2 + -12j + 6j2

Solving
6 + 15j = -2 + -12j + 6j2

Solving for variable 'j'.

Reorder the terms:
6 + 2 + 15j + 12j + -6j2 = -2 + -12j + 6j2 + 2 + 12j + -6j2

Combine like terms: 6 + 2 = 8
8 + 15j + 12j + -6j2 = -2 + -12j + 6j2 + 2 + 12j + -6j2

Combine like terms: 15j + 12j = 27j
8 + 27j + -6j2 = -2 + -12j + 6j2 + 2 + 12j + -6j2

Reorder the terms:
8 + 27j + -6j2 = -2 + 2 + -12j + 12j + 6j2 + -6j2

Combine like terms: -2 + 2 = 0
8 + 27j + -6j2 = 0 + -12j + 12j + 6j2 + -6j2
8 + 27j + -6j2 = -12j + 12j + 6j2 + -6j2

Combine like terms: -12j + 12j = 0
8 + 27j + -6j2 = 0 + 6j2 + -6j2
8 + 27j + -6j2 = 6j2 + -6j2

Combine like terms: 6j2 + -6j2 = 0
8 + 27j + -6j2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
-1.333333333 + -4.5j + j2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + -4.5j + 1.333333333 + j2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + -4.5j + j2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + -4.5j + j2 = 0 + 1.333333333
-4.5j + j2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
-4.5j + j2 = 1.333333333

The j term is -4.5j.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5j + 5.0625 + j2 = 1.333333333 + 5.0625

Reorder the terms:
5.0625 + -4.5j + j2 = 1.333333333 + 5.0625

Combine like terms: 1.333333333 + 5.0625 = 6.395833333
5.0625 + -4.5j + j2 = 6.395833333

Factor a perfect square on the left side:
(j + -2.25)(j + -2.25) = 6.395833333

Calculate the square root of the right side: 2.528998484

Break this problem into two subproblems by setting 
(j + -2.25) equal to 2.528998484 and -2.528998484.

Subproblem 1
j + -2.25 = 2.528998484

Simplifying
j + -2.25 = 2.528998484

Reorder the terms:
-2.25 + j = 2.528998484

Solving
-2.25 + j = 2.528998484

Solving for variable 'j'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + j = 2.528998484 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + j = 2.528998484 + 2.25
j = 2.528998484 + 2.25

Combine like terms: 2.528998484 + 2.25 = 4.778998484
j = 4.778998484

Simplifying
j = 4.778998484

Subproblem 2
j + -2.25 = -2.528998484

Simplifying
j + -2.25 = -2.528998484

Reorder the terms:
-2.25 + j = -2.528998484

Solving
-2.25 + j = -2.528998484

Solving for variable 'j'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + j = -2.528998484 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + j = -2.528998484 + 2.25
j = -2.528998484 + 2.25

Combine like terms: -2.528998484 + 2.25 = -0.278998484
j = -0.278998484

Simplifying
j = -0.278998484

Solution
The solution to the problem is based on the solutions
from the subproblems.
j = {4.778998484, -0.278998484}