14x^3+4x^2+10x=0

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Solution for 14x^3+4x^2+10x=0 equation: 


Simplifying
14x3 + 4x2 + 10x = 0

Reorder the terms:
10x + 4x2 + 14x3 = 0

Solving
10x + 4x2 + 14x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(5 + 2x + 7x2) = 0

Ignore the factor 2.

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 '(5 + 2x + 7x2)' equal to zero and attempt to solve:

Simplifying
5 + 2x + 7x2 = 0

Solving
5 + 2x + 7x2 = 0

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

Divide each side by '7'.
0.7142857143 + 0.2857142857x + x2 = 0

Move the constant term to the right:

Add '-0.7142857143' to each side of the equation.
0.7142857143 + 0.2857142857x + -0.7142857143 + x2 = 0 + -0.7142857143

Reorder the terms:
0.7142857143 + -0.7142857143 + 0.2857142857x + x2 = 0 + -0.7142857143

Combine like terms: 0.7142857143 + -0.7142857143 = 0.0000000000
0.0000000000 + 0.2857142857x + x2 = 0 + -0.7142857143
0.2857142857x + x2 = 0 + -0.7142857143

Combine like terms: 0 + -0.7142857143 = -0.7142857143
0.2857142857x + x2 = -0.7142857143

The x term is 0.2857142857x.  Take half its coefficient (0.1428571429).
Square it (0.02040816328) and add it to both sides.

Add '0.02040816328' to each side of the equation.
0.2857142857x + 0.02040816328 + x2 = -0.7142857143 + 0.02040816328

Reorder the terms:
0.02040816328 + 0.2857142857x + x2 = -0.7142857143 + 0.02040816328

Combine like terms: -0.7142857143 + 0.02040816328 = -0.69387755102
0.02040816328 + 0.2857142857x + x2 = -0.69387755102

Factor a perfect square on the left side:
(x + 0.1428571429)(x + 0.1428571429) = -0.69387755102

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}

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