4x^4+12x^3+29x^2=0

Solution for 4x^4+12x^3+29x^2=0 equation:

Simplifying
4x4 + 12x3 + 29x2 = 0

Reorder the terms:
29x2 + 12x3 + 4x4 = 0

Solving
29x2 + 12x3 + 4x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(29 + 12x + 4x2) = 0

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 '(29 + 12x + 4x2)' equal to zero and attempt to solve:

Simplifying
29 + 12x + 4x2 = 0

Solving
29 + 12x + 4x2 = 0

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

Divide each side by '4'.
7.25 + 3x + x2 = 0

Move the constant term to the right:

Add '-7.25' to each side of the equation.
7.25 + 3x + -7.25 + x2 = 0 + -7.25

Reorder the terms:
7.25 + -7.25 + 3x + x2 = 0 + -7.25

Combine like terms: 7.25 + -7.25 = 0.00
0.00 + 3x + x2 = 0 + -7.25
3x + x2 = 0 + -7.25

Combine like terms: 0 + -7.25 = -7.25
3x + x2 = -7.25

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = -7.25 + 2.25

Reorder the terms:
2.25 + 3x + x2 = -7.25 + 2.25

Combine like terms: -7.25 + 2.25 = -5
2.25 + 3x + x2 = -5

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = -5

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}