k^3-2k^2r-3kr^2=0

Solution for k^3-2k^2r-3kr^2=0 equation:

Simplifying
k3 + -2k2r + -3kr2 = 0

Reorder the terms:
-3kr2 + -2k2r + k3 = 0

Solving
-3kr2 + -2k2r + k3 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), 'k'.
k(-3r2 + -2kr + k2) = 0

Factor a trinomial.
k((-1r + -1k)(3r + -1k)) = 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 '(-1r + -1k)' equal to zero and attempt to solve:

Simplifying
-1r + -1k = 0

Reorder the terms:
-1k + -1r = 0

Solving
-1k + -1r = 0

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

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

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

Divide each side by '-1'.
k = -1r

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

Simplifying
3r + -1k = 0

Reorder the terms:
-1k + 3r = 0

Solving
-1k + 3r = 0

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

Add '-3r' to each side of the equation.
-1k + 3r + -3r = 0 + -3r

Combine like terms: 3r + -3r = 0
-1k + 0 = 0 + -3r
-1k = 0 + -3r
Remove the zero:
-1k = -3r

Divide each side by '-1'.
k = 3r

Simplifying
k = 3r
Solution
k = {0, -1r, 3r}