-6j^2-9j-3=0

Solution for -6j^2-9j-3=0 equation:

Simplifying
-6j2 + -9j + -3 = 0

Reorder the terms:
-3 + -9j + -6j2 = 0

Solving
-3 + -9j + -6j2 = 0

Solving for variable 'j'.

Factor out the Greatest Common Factor (GCF), '-3'.
-3(1 + 3j + 2j2) = 0

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

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

Simplifying
1 + j = 0

Solving
1 + j = 0

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

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

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

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

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

Simplifying
1 + 2j = 0

Solving
1 + 2j = 0

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

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

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

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

Divide each side by '2'.
j = -0.5

Simplifying
j = -0.5
Solution
j = {-1, -0.5}