12x^3+6x^2+13x=0

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Solution for 12x^3+6x^2+13x=0 equation: 


Simplifying
12x3 + 6x2 + 13x = 0

Reorder the terms:
13x + 6x2 + 12x3 = 0

Solving
13x + 6x2 + 12x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(13 + 6x + 12x2) = 0


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 '(13 + 6x + 12x2)' equal to zero and attempt to solve:

Simplifying
13 + 6x + 12x2 = 0

Solving
13 + 6x + 12x2 = 0

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

Divide each side by '12'.
1.083333333 + 0.5x + x2 = 0

Move the constant term to the right:

Add '-1.083333333' to each side of the equation.
1.083333333 + 0.5x + -1.083333333 + x2 = 0 + -1.083333333

Reorder the terms:
1.083333333 + -1.083333333 + 0.5x + x2 = 0 + -1.083333333

Combine like terms: 1.083333333 + -1.083333333 = 0.000000000
0.000000000 + 0.5x + x2 = 0 + -1.083333333
0.5x + x2 = 0 + -1.083333333

Combine like terms: 0 + -1.083333333 = -1.083333333
0.5x + x2 = -1.083333333

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 = -1.083333333 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = -1.083333333 + 0.0625

Combine like terms: -1.083333333 + 0.0625 = -1.020833333
0.0625 + 0.5x + x2 = -1.020833333

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = -1.020833333

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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