(-16x^4)-(32x^3)-(80x^2)=0

Solution for (-16x^4)-(32x^3)-(80x^2)=0 equation:

Simplifying
(-16x4) + -1(32x3) + -1(80x2) = 0

Remove parenthesis around (32x3)
(-16x4) + -1 * 32x3 + -1(80x2) = 0

Multiply -1 * 32
(-16x4) + -32x3 + -1(80x2) = 0

Remove parenthesis around (80x2)
(-16x4) + -32x3 + -1 * 80x2 = 0

Multiply -1 * 80
(-16x4) + -32x3 + -80x2 = 0

Reorder the terms:
-80x2 + -32x3 + (-16x4) = 0

Solving
-80x2 + -32x3 + (-16x4) = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-16x2'.
-16x2(5 + 2x + x2) = 0

Ignore the factor -16.
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 '(5 + 2x + x2)' equal to zero and attempt to solve:

Simplifying
5 + 2x + x2 = 0

Solving
5 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 2x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + 2x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2x + x2 = 0 + -5
2x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
2x + x2 = -5

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 = -5 + 1

Reorder the terms:
1 + 2x + x2 = -5 + 1

Combine like terms: -5 + 1 = -4
1 + 2x + x2 = -4

Factor a perfect square on the left side:
(x + 1)(x + 1) = -4

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}