j^2+5j=-4

Solution for j^2+5j=-4 equation:

Simplifying
j2 + 5j = -4

Reorder the terms:
5j + j2 = -4

Solving
5j + j2 = -4

Solving for variable 'j'.

Reorder the terms:
4 + 5j + j2 = -4 + 4

Combine like terms: -4 + 4 = 0
4 + 5j + j2 = 0

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

Subproblem 1
Set the factor '(4 + j)' equal to zero and attempt to solve:

Simplifying
4 + j = 0

Solving
4 + j = 0

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

Add '-4' to each side of the equation.
4 + -4 + j = 0 + -4

Combine like terms: 4 + -4 = 0
0 + j = 0 + -4
j = 0 + -4

Combine like terms: 0 + -4 = -4
j = -4

Simplifying
j = -4
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 = {-4, -1}