12x^4+4x^3+40x^2=0

Solution for 12x^4+4x^3+40x^2=0 equation:

Simplifying
12x4 + 4x3 + 40x2 = 0

Reorder the terms:
40x2 + 4x3 + 12x4 = 0

Solving
40x2 + 4x3 + 12x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x2'.
4x2(10 + x + 3x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}
Subproblem 2
Set the factor '(10 + x + 3x2)' equal to zero and attempt to solve:

Simplifying
10 + x + 3x2 = 0

Solving
10 + x + 3x2 = 0

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

Divide each side by '3'.
3.333333333 + 0.3333333333x + x2 = 0

Move the constant term to the right:

Add '-3.333333333' to each side of the equation.
3.333333333 + 0.3333333333x + -3.333333333 + x2 = 0 + -3.333333333

Reorder the terms:
3.333333333 + -3.333333333 + 0.3333333333x + x2 = 0 + -3.333333333

Combine like terms: 3.333333333 + -3.333333333 = 0.000000000
0.000000000 + 0.3333333333x + x2 = 0 + -3.333333333
0.3333333333x + x2 = 0 + -3.333333333

Combine like terms: 0 + -3.333333333 = -3.333333333
0.3333333333x + x2 = -3.333333333

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.
0.3333333333x + 0.25 + x2 = -3.333333333 + 0.25

Reorder the terms:
0.25 + 0.3333333333x + x2 = -3.333333333 + 0.25

Combine like terms: -3.333333333 + 0.25 = -3.083333333
0.25 + 0.3333333333x + x2 = -3.083333333

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -3.083333333

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}