12x^3+14x^2+10x=0

Solution for 12x^3+14x^2+10x=0 equation:

Simplifying
12x3 + 14x2 + 10x = 0

Reorder the terms:
10x + 14x2 + 12x3 = 0

Solving
10x + 14x2 + 12x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(5 + 7x + 6x2) = 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 + 7x + 6x2)' equal to zero and attempt to solve:

Simplifying
5 + 7x + 6x2 = 0

Solving
5 + 7x + 6x2 = 0

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

Divide each side by '6'.
0.8333333333 + 1.166666667x + x2 = 0

Move the constant term to the right:

Add '-0.8333333333' to each side of the equation.
0.8333333333 + 1.166666667x + -0.8333333333 + x2 = 0 + -0.8333333333

Reorder the terms:
0.8333333333 + -0.8333333333 + 1.166666667x + x2 = 0 + -0.8333333333

Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000
0.0000000000 + 1.166666667x + x2 = 0 + -0.8333333333
1.166666667x + x2 = 0 + -0.8333333333

Combine like terms: 0 + -0.8333333333 = -0.8333333333
1.166666667x + x2 = -0.8333333333

The x term is 1.166666667x.  Take half its coefficient (0.5833333335).
Square it (0.3402777780) and add it to both sides.

Add '0.3402777780' to each side of the equation.
1.166666667x + 0.3402777780 + x2 = -0.8333333333 + 0.3402777780

Reorder the terms:
0.3402777780 + 1.166666667x + x2 = -0.8333333333 + 0.3402777780

Combine like terms: -0.8333333333 + 0.3402777780 = -0.4930555553
0.3402777780 + 1.166666667x + x2 = -0.4930555553

Factor a perfect square on the left side:
(x + 0.5833333335)(x + 0.5833333335) = -0.4930555553

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}