36x^4+44x^3+24x^2=0

Solution for 36x^4+44x^3+24x^2=0 equation:

Simplifying
36x4 + 44x3 + 24x2 = 0

Reorder the terms:
24x2 + 44x3 + 36x4 = 0

Solving
24x2 + 44x3 + 36x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x2'.
4x2(6 + 11x + 9x2) = 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 '(6 + 11x + 9x2)' equal to zero and attempt to solve:

Simplifying
6 + 11x + 9x2 = 0

Solving
6 + 11x + 9x2 = 0

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

Divide each side by '9'.
0.6666666667 + 1.222222222x + x2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + 1.222222222x + -0.6666666667 + x2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + 1.222222222x + x2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + 1.222222222x + x2 = 0 + -0.6666666667
1.222222222x + x2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
1.222222222x + x2 = -0.6666666667

The x term is 1.222222222x.  Take half its coefficient (0.611111111).
Square it (0.3734567900) and add it to both sides.

Add '0.3734567900' to each side of the equation.
1.222222222x + 0.3734567900 + x2 = -0.6666666667 + 0.3734567900

Reorder the terms:
0.3734567900 + 1.222222222x + x2 = -0.6666666667 + 0.3734567900

Combine like terms: -0.6666666667 + 0.3734567900 = -0.2932098767
0.3734567900 + 1.222222222x + x2 = -0.2932098767

Factor a perfect square on the left side:
(x + 0.611111111)(x + 0.611111111) = -0.2932098767

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}