(2n+2)(2n+6)=

Solution for (2n+2)(2n+6)= equation:

Simplifying
(2n + 2)(2n + 6) = 0

Reorder the terms:
(2 + 2n)(2n + 6) = 0

Reorder the terms:
(2 + 2n)(6 + 2n) = 0

Multiply (2 + 2n) * (6 + 2n)
(2(6 + 2n) + 2n * (6 + 2n)) = 0
((6 * 2 + 2n * 2) + 2n * (6 + 2n)) = 0
((12 + 4n) + 2n * (6 + 2n)) = 0
(12 + 4n + (6 * 2n + 2n * 2n)) = 0
(12 + 4n + (12n + 4n2)) = 0

Combine like terms: 4n + 12n = 16n
(12 + 16n + 4n2) = 0

Solving
12 + 16n + 4n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '4'.
4(3 + 4n + n2) = 0

Factor a trinomial.
4((3 + n)(1 + n)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(3 + n)' equal to zero and attempt to solve:

Simplifying
3 + n = 0

Solving
3 + n = 0

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

Add '-3' to each side of the equation.
3 + -3 + n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + n = 0 + -3
n = 0 + -3

Combine like terms: 0 + -3 = -3
n = -3

Simplifying
n = -3
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 = {-3, -1}