2(n+3)n=-4

Solution for 2(n+3)n=-4 equation:

Simplifying
2(n + 3) * n = -4

Reorder the terms:
2(3 + n) * n = -4

Reorder the terms for easier multiplication:
2n(3 + n) = -4
(3 * 2n + n * 2n) = -4
(6n + 2n2) = -4

Solving
6n + 2n2 = -4

Solving for variable 'n'.

Reorder the terms:
4 + 6n + 2n2 = -4 + 4

Combine like terms: -4 + 4 = 0
4 + 6n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + 3n + n2) = 0

Factor a trinomial.
2((2 + n)(1 + n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(2 + n)' equal to zero and attempt to solve:

Simplifying
2 + n = 0

Solving
2 + n = 0

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

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

Combine like terms: 2 + -2 = 0
0 + n = 0 + -2
n = 0 + -2

Combine like terms: 0 + -2 = -2
n = -2

Simplifying
n = -2
Subproblem 2
Set the factor '(1 + n)' equal to zero and attempt to solve:

Simplifying
1 + n = 0

Solving
1 + n = 0

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

Add '-1' to each side of the equation.
1 + -1 + n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + n = 0 + -1
n = 0 + -1

Combine like terms: 0 + -1 = -1
n = -1

Simplifying
n = -1
Solution
n = {-2, -1}