n(n+1)=210

Solution for n(n+1)=210 equation:

Simplifying
n(n + 1) = 210

Reorder the terms:
n(1 + n) = 210
(1 * n + n * n) = 210
(1n + n2) = 210

Solving
1n + n2 = 210

Solving for variable 'n'.

Reorder the terms:
-210 + 1n + n2 = 210 + -210

Combine like terms: 210 + -210 = 0
-210 + 1n + n2 = 0

Factor a trinomial.
(-15 + -1n)(14 + -1n) = 0

Subproblem 1
Set the factor '(-15 + -1n)' equal to zero and attempt to solve:

Simplifying
-15 + -1n = 0

Solving
-15 + -1n = 0

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

Add '15' to each side of the equation.
-15 + 15 + -1n = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1n = 0 + 15
-1n = 0 + 15

Combine like terms: 0 + 15 = 15
-1n = 15

Divide each side by '-1'.
n = -15

Simplifying
n = -15
Subproblem 2
Set the factor '(14 + -1n)' equal to zero and attempt to solve:

Simplifying
14 + -1n = 0

Solving
14 + -1n = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1n = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1n = 0 + -14
-1n = 0 + -14

Combine like terms: 0 + -14 = -14
-1n = -14

Divide each side by '-1'.
n = 14

Simplifying
n = 14
Solution
n = {-15, 14}