2x^4+13x^3+32x^2=0

Solution for 2x^4+13x^3+32x^2=0 equation:

Simplifying
2x4 + 13x3 + 32x2 = 0

Reorder the terms:
32x2 + 13x3 + 2x4 = 0

Solving
32x2 + 13x3 + 2x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(32 + 13x + 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 '(32 + 13x + 2x2)' equal to zero and attempt to solve:

Simplifying
32 + 13x + 2x2 = 0

Solving
32 + 13x + 2x2 = 0

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

Divide each side by '2'.
16 + 6.5x + x2 = 0

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + 6.5x + -16 + x2 = 0 + -16

Reorder the terms:
16 + -16 + 6.5x + x2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + 6.5x + x2 = 0 + -16
6.5x + x2 = 0 + -16

Combine like terms: 0 + -16 = -16
6.5x + x2 = -16

The x term is 6.5x.  Take half its coefficient (3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
6.5x + 10.5625 + x2 = -16 + 10.5625

Reorder the terms:
10.5625 + 6.5x + x2 = -16 + 10.5625

Combine like terms: -16 + 10.5625 = -5.4375
10.5625 + 6.5x + x2 = -5.4375

Factor a perfect square on the left side:
(x + 3.25)(x + 3.25) = -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}