-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}