-16z^4-48z^3-64z^2=0

Solution for -16z^4-48z^3-64z^2=0 equation:

Simplifying
-16z4 + -48z3 + -64z2 = 0

Reorder the terms:
-64z2 + -48z3 + -16z4 = 0

Solving
-64z2 + -48z3 + -16z4 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '-16z2'.
-16z2(4 + 3z + z2) = 0

Ignore the factor -16.
Subproblem 1
Set the factor 'z2' equal to zero and attempt to solve:

Simplifying
z2 = 0

Solving
z2 = 0

Move all terms containing z to the left, all other terms to the right.

Simplifying
z2 = 0

Take the square root of each side:
z = {0}
Subproblem 2
Set the factor '(4 + 3z + z2)' equal to zero and attempt to solve:

Simplifying
4 + 3z + z2 = 0

Solving
4 + 3z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 3z + -4 + z2 = 0 + -4

Reorder the terms:
4 + -4 + 3z + z2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3z + z2 = 0 + -4
3z + z2 = 0 + -4

Combine like terms: 0 + -4 = -4
3z + z2 = -4

The z term is 3z.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3z + 2.25 + z2 = -4 + 2.25

Reorder the terms:
2.25 + 3z + z2 = -4 + 2.25

Combine like terms: -4 + 2.25 = -1.75
2.25 + 3z + z2 = -1.75

Factor a perfect square on the left side:
(z + 1.5)(z + 1.5) = -1.75

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
z = {0}