(-kx^2)+k^3=0

Solution for (-kx^2)+k^3=0 equation:

Simplifying
(-1kx2) + k3 = 0

Solving
(-1kx2) + k3 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), 'k'.
k((-1x2) + k2) = 0

Factor a difference between two squares.
k((x + k)((-1x) + k)) = 0

Subproblem 1
Set the factor 'k' equal to zero and attempt to solve:

Simplifying
k = 0

Solving
k = 0

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

Simplifying
k = 0
Subproblem 2
Set the factor '(x + k)' equal to zero and attempt to solve:

Simplifying
x + k = 0

Reorder the terms:
k + x = 0

Solving
k + x = 0

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

Add '-1x' to each side of the equation.
k + x + -1x = 0 + -1x

Combine like terms: x + -1x = 0
k + 0 = 0 + -1x
k = 0 + -1x
Remove the zero:
k = -1x

Simplifying
k = -1x
Subproblem 3
Set the factor '((-1x) + k)' equal to zero and attempt to solve:

Simplifying
(-1x) + k = 0

Reorder the terms:
k + (-1x) = 0

Solving
k + (-1x) = 0

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

Add '(x)' to each side of the equation.
k + (-1x) + (x) = 0 + (x)
k + (-1x) + x = 0 + (x)

Combine like terms: (-1x) + x = 0
k + 0 = 0 + (x)
k = 0 + (x)
k = 0 + x
Remove the zero:
k = x

Simplifying
k = x
Solution
k = {0, -1x, x}