j-15j+8=-3(4j-3)2j-1

Solution for j-15j+8=-3(4j-3)2j-1 equation:

Simplifying
j + -15j + 8 = -3(4j + -3) * 2j + -1

Reorder the terms:
8 + j + -15j = -3(4j + -3) * 2j + -1

Combine like terms: j + -15j = -14j
8 + -14j = -3(4j + -3) * 2j + -1

Reorder the terms:
8 + -14j = -3(-3 + 4j) * 2j + -1

Reorder the terms for easier multiplication:
8 + -14j = -3 * 2j(-3 + 4j) + -1

Multiply -3 * 2
8 + -14j = -6j(-3 + 4j) + -1
8 + -14j = (-3 * -6j + 4j * -6j) + -1
8 + -14j = (18j + -24j2) + -1

Reorder the terms:
8 + -14j = -1 + 18j + -24j2

Solving
8 + -14j = -1 + 18j + -24j2

Solving for variable 'j'.

Reorder the terms:
8 + 1 + -14j + -18j + 24j2 = -1 + 18j + -24j2 + 1 + -18j + 24j2

Combine like terms: 8 + 1 = 9
9 + -14j + -18j + 24j2 = -1 + 18j + -24j2 + 1 + -18j + 24j2

Combine like terms: -14j + -18j = -32j
9 + -32j + 24j2 = -1 + 18j + -24j2 + 1 + -18j + 24j2

Reorder the terms:
9 + -32j + 24j2 = -1 + 1 + 18j + -18j + -24j2 + 24j2

Combine like terms: -1 + 1 = 0
9 + -32j + 24j2 = 0 + 18j + -18j + -24j2 + 24j2
9 + -32j + 24j2 = 18j + -18j + -24j2 + 24j2

Combine like terms: 18j + -18j = 0
9 + -32j + 24j2 = 0 + -24j2 + 24j2
9 + -32j + 24j2 = -24j2 + 24j2

Combine like terms: -24j2 + 24j2 = 0
9 + -32j + 24j2 = 0

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

Divide each side by '24'.
0.375 + -1.333333333j + j2 = 0

Move the constant term to the right:

Add '-0.375' to each side of the equation.
0.375 + -1.333333333j + -0.375 + j2 = 0 + -0.375

Reorder the terms:
0.375 + -0.375 + -1.333333333j + j2 = 0 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + -1.333333333j + j2 = 0 + -0.375
-1.333333333j + j2 = 0 + -0.375

Combine like terms: 0 + -0.375 = -0.375
-1.333333333j + j2 = -0.375

The j term is -1.333333333j.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333j + 0.4444444442 + j2 = -0.375 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333j + j2 = -0.375 + 0.4444444442

Combine like terms: -0.375 + 0.4444444442 = 0.0694444442
0.4444444442 + -1.333333333j + j2 = 0.0694444442

Factor a perfect square on the left side:
(j + -0.6666666665)(j + -0.6666666665) = 0.0694444442

Calculate the square root of the right side: 0.263523138

Break this problem into two subproblems by setting 
(j + -0.6666666665) equal to 0.263523138 and -0.263523138.

Subproblem 1
j + -0.6666666665 = 0.263523138

Simplifying
j + -0.6666666665 = 0.263523138

Reorder the terms:
-0.6666666665 + j = 0.263523138

Solving
-0.6666666665 + j = 0.263523138

Solving for variable 'j'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + j = 0.263523138 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + j = 0.263523138 + 0.6666666665
j = 0.263523138 + 0.6666666665

Combine like terms: 0.263523138 + 0.6666666665 = 0.9301898045
j = 0.9301898045

Simplifying
j = 0.9301898045

Subproblem 2
j + -0.6666666665 = -0.263523138

Simplifying
j + -0.6666666665 = -0.263523138

Reorder the terms:
-0.6666666665 + j = -0.263523138

Solving
-0.6666666665 + j = -0.263523138

Solving for variable 'j'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + j = -0.263523138 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + j = -0.263523138 + 0.6666666665
j = -0.263523138 + 0.6666666665

Combine like terms: -0.263523138 + 0.6666666665 = 0.4031435285
j = 0.4031435285

Simplifying
j = 0.4031435285

Solution
The solution to the problem is based on the solutions
from the subproblems.
j = {0.9301898045, 0.4031435285}