2n(n+2)=n^2+5

Solution for 2n(n+2)=n^2+5 equation:

Simplifying
2n(n + 2) = n2 + 5

Reorder the terms:
2n(2 + n) = n2 + 5
(2 * 2n + n * 2n) = n2 + 5
(4n + 2n2) = n2 + 5

Reorder the terms:
4n + 2n2 = 5 + n2

Solving
4n + 2n2 = 5 + n2

Solving for variable 'n'.

Reorder the terms:
-5 + 4n + 2n2 + -1n2 = 5 + n2 + -5 + -1n2

Combine like terms: 2n2 + -1n2 = 1n2
-5 + 4n + 1n2 = 5 + n2 + -5 + -1n2

Reorder the terms:
-5 + 4n + 1n2 = 5 + -5 + n2 + -1n2

Combine like terms: 5 + -5 = 0
-5 + 4n + 1n2 = 0 + n2 + -1n2
-5 + 4n + 1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
-5 + 4n + 1n2 = 0

Factor a trinomial.
(-5 + -1n)(1 + -1n) = 0

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

Simplifying
-5 + -1n = 0

Solving
-5 + -1n = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1n = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1n = 0 + 5
-1n = 0 + 5

Combine like terms: 0 + 5 = 5
-1n = 5

Divide each side by '-1'.
n = -5

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