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

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

Simplifying
2x4 + 2x3 + 24x2 = 0

Reorder the terms:
24x2 + 2x3 + 2x4 = 0

Solving
24x2 + 2x3 + 2x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x2'.
2x2(12 + x + x2) = 0

Ignore the factor 2.
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 '(12 + x + x2)' equal to zero and attempt to solve:

Simplifying
12 + x + x2 = 0

Solving
12 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + x + -12 + x2 = 0 + -12

Reorder the terms:
12 + -12 + x + x2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + x + x2 = 0 + -12
x + x2 = 0 + -12

Combine like terms: 0 + -12 = -12
x + x2 = -12

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.
x + 0.25 + x2 = -12 + 0.25

Reorder the terms:
0.25 + x + x2 = -12 + 0.25

Combine like terms: -12 + 0.25 = -11.75
0.25 + x + x2 = -11.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -11.75

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}