3j^2+11j+6=0

Solution for 3j^2+11j+6=0 equation:

Simplifying
3j2 + 11j + 6 = 0

Reorder the terms:
6 + 11j + 3j2 = 0

Solving
6 + 11j + 3j2 = 0

Solving for variable 'j'.

Factor a trinomial.
(3 + j)(2 + 3j) = 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 '(2 + 3j)' equal to zero and attempt to solve:

Simplifying
2 + 3j = 0

Solving
2 + 3j = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3j = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3j = 0 + -2
3j = 0 + -2

Combine like terms: 0 + -2 = -2
3j = -2

Divide each side by '3'.
j = -0.6666666667

Simplifying
j = -0.6666666667
Solution
j = {-3, -0.6666666667}