20=n(n+1)

Solution for 20=n(n+1) equation:

Simplifying
20 = n(n + 1)

Reorder the terms:
20 = n(1 + n)
20 = (1 * n + n * n)
20 = (1n + n2)

Solving
20 = 1n + n2

Solving for variable 'n'.

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

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

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

Factor a trinomial.
(4 + -1n)(5 + n) = 0

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

Simplifying
4 + -1n = 0

Solving
4 + -1n = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1n = 0 + -4

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

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

Divide each side by '-1'.
n = 4

Simplifying
n = 4
Subproblem 2
Set the factor '(5 + n)' equal to zero and attempt to solve:

Simplifying
5 + n = 0

Solving
5 + n = 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 + n = 0 + -5

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

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

Simplifying
n = -5
Solution
n = {4, -5}