14x^3-7x^2+21x=0

Solution for 14x^3-7x^2+21x=0 equation:

Simplifying
14x3 + -7x2 + 21x = 0

Reorder the terms:
21x + -7x2 + 14x3 = 0

Solving
21x + -7x2 + 14x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7x'.
7x(3 + -1x + 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 '(3 + -1x + 2x2)' equal to zero and attempt to solve:

Simplifying
3 + -1x + 2x2 = 0

Solving
3 + -1x + 2x2 = 0

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

Divide each side by '2'.
1.5 + -0.5x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -0.5x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -0.5x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -0.5x + x2 = 0 + -1.5
-0.5x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-0.5x + x2 = -1.5

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = -1.5 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = -1.5 + 0.0625

Combine like terms: -1.5 + 0.0625 = -1.4375
0.0625 + -0.5x + x2 = -1.4375

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = -1.4375

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}