-j^2+6j-9=0

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

Simplifying
-1j2 + 6j + -9 = 0

Reorder the terms:
-9 + 6j + -1j2 = 0

Solving
-9 + 6j + -1j2 = 0

Solving for variable 'j'.

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

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

Simplifying
-3 + j = 0

Solving
-3 + j = 0

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

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

Combine like terms: -3 + 3 = 0
0 + j = 0 + 3
j = 0 + 3

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

Simplifying
j = 3
Subproblem 2
Set the factor '(3 + -1j)' equal to zero and attempt to solve:

Simplifying
3 + -1j = 0

Solving
3 + -1j = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1j = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1j = 0 + -3
-1j = 0 + -3

Combine like terms: 0 + -3 = -3
-1j = -3

Divide each side by '-1'.
j = 3

Simplifying
j = 3
Solution
j = {3, 3}