2n^3+2n^2+2n=n*14

Solution for 2n^3+2n^2+2n=n*14 equation:

Simplifying
2n3 + 2n2 + 2n = n * 14

Reorder the terms:
2n + 2n2 + 2n3 = n * 14

Reorder the terms for easier multiplication:
2n + 2n2 + 2n3 = 14n

Solving
2n + 2n2 + 2n3 = 14n

Solving for variable 'n'.

Reorder the terms:
2n + -14n + 2n2 + 2n3 = 14n + -14n

Combine like terms: 2n + -14n = -12n
-12n + 2n2 + 2n3 = 14n + -14n

Combine like terms: 14n + -14n = 0
-12n + 2n2 + 2n3 = 0

Factor out the Greatest Common Factor (GCF), '2n'.
2n(-6 + n + n2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0
Subproblem 2
Set the factor '(-3 + -1n)' equal to zero and attempt to solve:

Simplifying
-3 + -1n = 0

Solving
-3 + -1n = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1n = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1n = 0 + 3
-1n = 0 + 3

Combine like terms: 0 + 3 = 3
-1n = 3

Divide each side by '-1'.
n = -3

Simplifying
n = -3
Subproblem 3
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 = {0, -3, 2}