14n^3+7n+7n^2=

Solution for 14n^3+7n+7n^2= equation:

Simplifying
14n3 + 7n + 7n2 = 0

Reorder the terms:
7n + 7n2 + 14n3 = 0

Solving
7n + 7n2 + 14n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '7n'.
7n(1 + n + 2n2) = 0

Ignore the factor 7.
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 '(1 + n + 2n2)' equal to zero and attempt to solve:

Simplifying
1 + n + 2n2 = 0

Solving
1 + n + 2n2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
0.5 + 0.5n + n2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 0.5n + -0.5 + n2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 0.5n + n2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 0.5n + n2 = 0 + -0.5
0.5n + n2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
0.5n + n2 = -0.5

The n term is n.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.5n + 0.25 + n2 = -0.5 + 0.25

Reorder the terms:
0.25 + 0.5n + n2 = -0.5 + 0.25

Combine like terms: -0.5 + 0.25 = -0.25
0.25 + 0.5n + n2 = -0.25

Factor a perfect square on the left side:
(n + 0.5)(n + 0.5) = -0.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
n = {0}