2n(n+2)=6

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

Simplifying
2n(n + 2) = 6

Reorder the terms:
2n(2 + n) = 6
(2 * 2n + n * 2n) = 6
(4n + 2n2) = 6

Solving
4n + 2n2 = 6

Solving for variable 'n'.

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

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

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

Factor a trinomial.
2((-3 + -1n)(1 + -1n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -1n)' equal to zero and attempt to solve:

Simplifying
-3 + -1n = 0

Solving
-3 + -1n = 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 + -1n = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1n = 0 + 3
-1n = 0 + 3

Combine like terms: 0 + 3 = 3
-1n = 3

Divide each side by '-1'.
n = -3

Simplifying
n = -3
Subproblem 2
Set the factor '(1 + -1n)' equal to zero and attempt to solve:

Simplifying
1 + -1n = 0

Solving
1 + -1n = 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 + -1n = 0 + -1

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

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

Divide each side by '-1'.
n = 1

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