14X^3+7X^2+7X=0

Solution for 14X^3+7X^2+7X=0 equation:

Simplifying
14X3 + 7X2 + 7X = 0

Reorder the terms:
7X + 7X2 + 14X3 = 0

Solving
7X + 7X2 + 14X3 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '7X'.
7X(1 + X + 2X2) = 0

Ignore the factor 7.
Subproblem 1
Set the factor 'X' equal to zero and attempt to solve:

Simplifying
X = 0

Solving
X = 0

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

Simplifying
X = 0
Subproblem 2
Set the factor '(1 + X + 2X2)' equal to zero and attempt to solve:

Simplifying
1 + X + 2X2 = 0

Solving
1 + X + 2X2 = 0

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

Divide each side by '2'.
0.5 + 0.5X + X2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 0.5X + -0.5 + X2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 0.5X + X2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 0.5X + X2 = 0 + -0.5
0.5X + X2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
0.5X + X2 = -0.5

The X term is X.  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.
0.5X + 0.25 + X2 = -0.5 + 0.25

Reorder the terms:
0.25 + 0.5X + X2 = -0.5 + 0.25

Combine like terms: -0.5 + 0.25 = -0.25
0.25 + 0.5X + X2 = -0.25

Factor a perfect square on the left side:
(X + 0.5)(X + 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
X = {0}