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

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

Simplifying
x4 + 2x3 + 3x2 = 0

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

Solving
3x2 + 2x3 + x4 = 0

Solving for variable 'x'.

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

Simplifying
3 + 2x + x2 = 0

Solving
3 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 2x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + 2x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x + x2 = 0 + -3
2x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
2x + x2 = -3

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = -3 + 1

Reorder the terms:
1 + 2x + x2 = -3 + 1

Combine like terms: -3 + 1 = -2
1 + 2x + x2 = -2

Factor a perfect square on the left side:
(x + 1)(x + 1) = -2

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}