n+(n+1)(n+2)=14

Solution for n+(n+1)(n+2)=14 equation:

Simplifying
n + (n + 1)(n + 2) = 14

Reorder the terms:
n + (1 + n)(n + 2) = 14

Reorder the terms:
n + (1 + n)(2 + n) = 14

Multiply (1 + n) * (2 + n)
n + (1(2 + n) + n(2 + n)) = 14
n + ((2 * 1 + n * 1) + n(2 + n)) = 14
n + ((2 + 1n) + n(2 + n)) = 14
n + (2 + 1n + (2 * n + n * n)) = 14
n + (2 + 1n + (2n + n2)) = 14

Combine like terms: 1n + 2n = 3n
n + (2 + 3n + n2) = 14

Reorder the terms:
2 + n + 3n + n2 = 14

Combine like terms: n + 3n = 4n
2 + 4n + n2 = 14

Solving
2 + 4n + n2 = 14

Solving for variable 'n'.

Reorder the terms:
2 + -14 + 4n + n2 = 14 + -14

Combine like terms: 2 + -14 = -12
-12 + 4n + n2 = 14 + -14

Combine like terms: 14 + -14 = 0
-12 + 4n + n2 = 0

Factor a trinomial.
(-6 + -1n)(2 + -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 '(2 + -1n)' equal to zero and attempt to solve:

Simplifying
2 + -1n = 0

Solving
2 + -1n = 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 + -1n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1n = 0 + -2
-1n = 0 + -2

Combine like terms: 0 + -2 = -2
-1n = -2

Divide each side by '-1'.
n = 2

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