2n(n+4)=n^2+20

Solution for 2n(n+4)=n^2+20 equation:

Simplifying
2n(n + 4) = n2 + 20

Reorder the terms:
2n(4 + n) = n2 + 20
(4 * 2n + n * 2n) = n2 + 20
(8n + 2n2) = n2 + 20

Reorder the terms:
8n + 2n2 = 20 + n2

Solving
8n + 2n2 = 20 + n2

Solving for variable 'n'.

Reorder the terms:
-20 + 8n + 2n2 + -1n2 = 20 + n2 + -20 + -1n2

Combine like terms: 2n2 + -1n2 = 1n2
-20 + 8n + 1n2 = 20 + n2 + -20 + -1n2

Reorder the terms:
-20 + 8n + 1n2 = 20 + -20 + n2 + -1n2

Combine like terms: 20 + -20 = 0
-20 + 8n + 1n2 = 0 + n2 + -1n2
-20 + 8n + 1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
-20 + 8n + 1n2 = 0

Factor a trinomial.
(-10 + -1n)(2 + -1n) = 0

Subproblem 1
Set the factor '(-10 + -1n)' equal to zero and attempt to solve:

Simplifying
-10 + -1n = 0

Solving
-10 + -1n = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1n = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1n = 0 + 10
-1n = 0 + 10

Combine like terms: 0 + 10 = 10
-1n = 10

Divide each side by '-1'.
n = -10

Simplifying
n = -10
Subproblem 2
Set the factor '(2 + -1n)' equal to zero and attempt to solve:

Simplifying
2 + -1n = 0

Solving
2 + -1n = 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 + -1n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1n = 0 + -2
-1n = 0 + -2

Combine like terms: 0 + -2 = -2
-1n = -2

Divide each side by '-1'.
n = 2

Simplifying
n = 2
Solution
n = {-10, 2}