27k=(3k)(3k)(3k)

Solution for 27k=(3k)(3k)(3k) equation:

Simplifying
27k = (3k)(3k)(3k)

Remove parenthesis around (3k)
27k = 3k(3k)(3k)

Remove parenthesis around (3k)
27k = 3k * 3k(3k)

Remove parenthesis around (3k)
27k = 3k * 3k * 3k

Reorder the terms for easier multiplication:
27k = 3 * 3 * 3k * k * k

Multiply 3 * 3
27k = 9 * 3k * k * k

Multiply 9 * 3
27k = 27k * k * k

Multiply k * k
27k = 27k2 * k

Multiply k2 * k
27k = 27k3

Solving
27k = 27k3

Solving for variable 'k'.

Combine like terms: 27k3 + -27k3 = 0
27k + -27k3 = 0

Factor out the Greatest Common Factor (GCF), '27k'.
27k(1 + -1k2) = 0

Factor a difference between two squares.
27k((1 + k)(1 + -1k)) = 0

Ignore the factor 27.
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 '(1 + k)' equal to zero and attempt to solve:

Simplifying
1 + k = 0

Solving
1 + k = 0

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

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

Combine like terms: 1 + -1 = 0
0 + k = 0 + -1
k = 0 + -1

Combine like terms: 0 + -1 = -1
k = -1

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

Simplifying
1 + -1k = 0

Solving
1 + -1k = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1k = 0 + -1
-1k = 0 + -1

Combine like terms: 0 + -1 = -1
-1k = -1

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

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