12n(n+1)=n-2

Solution for 12n(n+1)=n-2 equation:

Simplifying
12n(n + 1) = n + -2

Reorder the terms:
12n(1 + n) = n + -2
(1 * 12n + n * 12n) = n + -2
(12n + 12n2) = n + -2

Reorder the terms:
12n + 12n2 = -2 + n

Solving
12n + 12n2 = -2 + n

Solving for variable 'n'.

Reorder the terms:
2 + 12n + -1n + 12n2 = -2 + n + 2 + -1n

Combine like terms: 12n + -1n = 11n
2 + 11n + 12n2 = -2 + n + 2 + -1n

Reorder the terms:
2 + 11n + 12n2 = -2 + 2 + n + -1n

Combine like terms: -2 + 2 = 0
2 + 11n + 12n2 = 0 + n + -1n
2 + 11n + 12n2 = n + -1n

Combine like terms: n + -1n = 0
2 + 11n + 12n2 = 0

Factor a trinomial.
(2 + 3n)(1 + 4n) = 0

Subproblem 1
Set the factor '(2 + 3n)' equal to zero and attempt to solve:

Simplifying
2 + 3n = 0

Solving
2 + 3n = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3n = 0 + -2
3n = 0 + -2

Combine like terms: 0 + -2 = -2
3n = -2

Divide each side by '3'.
n = -0.6666666667

Simplifying
n = -0.6666666667
Subproblem 2
Set the factor '(1 + 4n)' equal to zero and attempt to solve:

Simplifying
1 + 4n = 0

Solving
1 + 4n = 0

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

Add '-1' to each side of the equation.
1 + -1 + 4n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4n = 0 + -1
4n = 0 + -1

Combine like terms: 0 + -1 = -1
4n = -1

Divide each side by '4'.
n = -0.25

Simplifying
n = -0.25
Solution
n = {-0.6666666667, -0.25}