n(n+1)=30

Solution for n(n+1)=30 equation:

Simplifying
n(n + 1) = 30

Reorder the terms:
n(1 + n) = 30
(1 * n + n * n) = 30
(1n + n2) = 30

Solving
1n + n2 = 30

Solving for variable 'n'.

Reorder the terms:
-30 + 1n + n2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + 1n + n2 = 0

Factor a trinomial.
(-6 + -1n)(5 + -1n) = 0

Subproblem 1
Set the factor '(-6 + -1n)' equal to zero and attempt to solve:

Simplifying
-6 + -1n = 0

Solving
-6 + -1n = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1n = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1n = 0 + 6
-1n = 0 + 6

Combine like terms: 0 + 6 = 6
-1n = 6

Divide each side by '-1'.
n = -6

Simplifying
n = -6
Subproblem 2
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
Solution
n = {-6, 5}