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

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

Simplifying
2x4 + 3x3 + 4x2 = 0

Reorder the terms:
4x2 + 3x3 + 2x4 = 0

Solving
4x2 + 3x3 + 2x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(4 + 3x + 2x2) = 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 '(4 + 3x + 2x2)' equal to zero and attempt to solve:

Simplifying
4 + 3x + 2x2 = 0

Solving
4 + 3x + 2x2 = 0

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

Divide each side by '2'.
2 + 1.5x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 1.5x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + 1.5x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 1.5x + x2 = 0 + -2
1.5x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
1.5x + x2 = -2

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = -2 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = -2 + 0.5625

Combine like terms: -2 + 0.5625 = -1.4375
0.5625 + 1.5x + x2 = -1.4375

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = -1.4375

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}