3n(n+1)=126

Solution for 3n(n+1)=126 equation:

Simplifying
3n(n + 1) = 126

Reorder the terms:
3n(1 + n) = 126
(1 * 3n + n * 3n) = 126
(3n + 3n2) = 126

Solving
3n + 3n2 = 126

Solving for variable 'n'.

Reorder the terms:
-126 + 3n + 3n2 = 126 + -126

Combine like terms: 126 + -126 = 0
-126 + 3n + 3n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-42 + n + n2) = 0

Factor a trinomial.
3((-7 + -1n)(6 + -1n)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-7 + -1n)' equal to zero and attempt to solve:

Simplifying
-7 + -1n = 0

Solving
-7 + -1n = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1n = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1n = 0 + 7
-1n = 0 + 7

Combine like terms: 0 + 7 = 7
-1n = 7

Divide each side by '-1'.
n = -7

Simplifying
n = -7
Subproblem 2
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
Solution
n = {-7, 6}