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

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

Simplifying
12x2 + 2x4 + 3x3 = 0

Reorder the terms:
12x2 + 3x3 + 2x4 = 0

Solving
12x2 + 3x3 + 2x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(12 + 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 '(12 + 3x + 2x2)' equal to zero and attempt to solve:

Simplifying
12 + 3x + 2x2 = 0

Solving
12 + 3x + 2x2 = 0

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

Divide each side by '2'.
6 + 1.5x + x2 = 0

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 1.5x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + 1.5x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 1.5x + x2 = 0 + -6
1.5x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
1.5x + x2 = -6

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 = -6 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = -6 + 0.5625

Combine like terms: -6 + 0.5625 = -5.4375
0.5625 + 1.5x + x2 = -5.4375

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = -5.4375

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}