-3(j+3)9j=-15

Solution for -3(j+3)9j=-15 equation:

Simplifying
-3(j + 3) * 9j = -15

Reorder the terms:
-3(3 + j) * 9j = -15

Reorder the terms for easier multiplication:
-3 * 9j(3 + j) = -15

Multiply -3 * 9
-27j(3 + j) = -15
(3 * -27j + j * -27j) = -15
(-81j + -27j2) = -15

Solving
-81j + -27j2 = -15

Solving for variable 'j'.

Reorder the terms:
15 + -81j + -27j2 = -15 + 15

Combine like terms: -15 + 15 = 0
15 + -81j + -27j2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(5 + -27j + -9j2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(5 + -27j + -9j2)' equal to zero and attempt to solve:

Simplifying
5 + -27j + -9j2 = 0

Solving
5 + -27j + -9j2 = 0

Begin completing the square.  Divide all terms by
-9 the coefficient of the squared term: 

Divide each side by '-9'.
-0.5555555556 + 3j + j2 = 0

Move the constant term to the right:

Add '0.5555555556' to each side of the equation.
-0.5555555556 + 3j + 0.5555555556 + j2 = 0 + 0.5555555556

Reorder the terms:
-0.5555555556 + 0.5555555556 + 3j + j2 = 0 + 0.5555555556

Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000
0.0000000000 + 3j + j2 = 0 + 0.5555555556
3j + j2 = 0 + 0.5555555556

Combine like terms: 0 + 0.5555555556 = 0.5555555556
3j + j2 = 0.5555555556

The j term is 3j.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3j + 2.25 + j2 = 0.5555555556 + 2.25

Reorder the terms:
2.25 + 3j + j2 = 0.5555555556 + 2.25

Combine like terms: 0.5555555556 + 2.25 = 2.8055555556
2.25 + 3j + j2 = 2.8055555556

Factor a perfect square on the left side:
(j + 1.5)(j + 1.5) = 2.8055555556

Calculate the square root of the right side: 1.67497927

Break this problem into two subproblems by setting 
(j + 1.5) equal to 1.67497927 and -1.67497927.

Subproblem 1
j + 1.5 = 1.67497927

Simplifying
j + 1.5 = 1.67497927

Reorder the terms:
1.5 + j = 1.67497927

Solving
1.5 + j = 1.67497927

Solving for variable 'j'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + j = 1.67497927 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + j = 1.67497927 + -1.5
j = 1.67497927 + -1.5

Combine like terms: 1.67497927 + -1.5 = 0.17497927
j = 0.17497927

Simplifying
j = 0.17497927

Subproblem 2
j + 1.5 = -1.67497927

Simplifying
j + 1.5 = -1.67497927

Reorder the terms:
1.5 + j = -1.67497927

Solving
1.5 + j = -1.67497927

Solving for variable 'j'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + j = -1.67497927 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + j = -1.67497927 + -1.5
j = -1.67497927 + -1.5

Combine like terms: -1.67497927 + -1.5 = -3.17497927
j = -3.17497927

Simplifying
j = -3.17497927

Solution
The solution to the problem is based on the solutions
from the subproblems.
j = {0.17497927, -3.17497927}
Solution
j = {0.17497927, -3.17497927}