3j^2+6j+3=0

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

Simplifying
3j2 + 6j + 3 = 0

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

Solving
3 + 6j + 3j2 = 0

Solving for variable 'j'.

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

Factor a trinomial.
3((1 + j)(1 + j)) = 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 + 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
Solution
j = {-1, -1}