2k^3-50k=0

Solution for 2k^3-50k=0 equation:

Simplifying
2k3 + -50k = 0

Reorder the terms:
-50k + 2k3 = 0

Solving
-50k + 2k3 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '2k'.
2k(-25 + k2) = 0

Factor a difference between two squares.
2k((5 + k)(-5 + k)) = 0

Ignore the factor 2.
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 '(5 + k)' equal to zero and attempt to solve:

Simplifying
5 + k = 0

Solving
5 + k = 0

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

Add '-5' to each side of the equation.
5 + -5 + k = 0 + -5

Combine like terms: 5 + -5 = 0
0 + k = 0 + -5
k = 0 + -5

Combine like terms: 0 + -5 = -5
k = -5

Simplifying
k = -5
Subproblem 3
Set the factor '(-5 + k)' equal to zero and attempt to solve:

Simplifying
-5 + k = 0

Solving
-5 + k = 0

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

Add '5' to each side of the equation.
-5 + 5 + k = 0 + 5

Combine like terms: -5 + 5 = 0
0 + k = 0 + 5
k = 0 + 5

Combine like terms: 0 + 5 = 5
k = 5

Simplifying
k = 5
Solution
k = {0, -5, 5}