n(n+1)=420

Solution for n(n+1)=420 equation:

Simplifying
n(n + 1) = 420

Reorder the terms:
n(1 + n) = 420
(1 * n + n * n) = 420
(1n + n2) = 420

Solving
1n + n2 = 420

Solving for variable 'n'.

Reorder the terms:
-420 + 1n + n2 = 420 + -420

Combine like terms: 420 + -420 = 0
-420 + 1n + n2 = 0

Factor a trinomial.
(-21 + -1n)(20 + -1n) = 0

Subproblem 1
Set the factor '(-21 + -1n)' equal to zero and attempt to solve:

Simplifying
-21 + -1n = 0

Solving
-21 + -1n = 0

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

Add '21' to each side of the equation.
-21 + 21 + -1n = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -1n = 0 + 21
-1n = 0 + 21

Combine like terms: 0 + 21 = 21
-1n = 21

Divide each side by '-1'.
n = -21

Simplifying
n = -21
Subproblem 2
Set the factor '(20 + -1n)' equal to zero and attempt to solve:

Simplifying
20 + -1n = 0

Solving
20 + -1n = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1n = 0 + -20

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

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

Divide each side by '-1'.
n = 20

Simplifying
n = 20
Solution
n = {-21, 20}