j^2+6j+5=0

Solution for j^2+6j+5=0 equation:

Simplifying
j2 + 6j + 5 = 0

Reorder the terms:
5 + 6j + j2 = 0

Solving
5 + 6j + j2 = 0

Solving for variable 'j'.

Factor a trinomial.
(5 + j)(1 + j) = 0

Subproblem 1
Set the factor '(5 + j)' equal to zero and attempt to solve:

Simplifying
5 + j = 0

Solving
5 + j = 0

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

Add '-5' to each side of the equation.
5 + -5 + j = 0 + -5

Combine like terms: 5 + -5 = 0
0 + j = 0 + -5
j = 0 + -5

Combine like terms: 0 + -5 = -5
j = -5

Simplifying
j = -5
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 = {-5, -1}