(n)(n+1)=20

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

Simplifying
(n)(n + 1) = 20

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

Solving
1n + n2 = 20

Solving for variable 'n'.

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

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

Factor a trinomial.
(-5 + -1n)(4 + -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 '(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
Solution
n = {-5, 4}