j^2+6j=-9

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

Simplifying
j2 + 6j = -9

Reorder the terms:
6j + j2 = -9

Solving
6j + j2 = -9

Solving for variable 'j'.

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

Combine like terms: -9 + 9 = 0
9 + 6j + j2 = 0

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