find anumber k satisfying the given condition.

6(-2/3)cube-4(-2/3)sq+k(-2/3)-k

To find the value of "k" that satisfies the given condition in the equation:

6(-2/3)^3 - 4(-2/3)^2 + k(-2/3) - k

Let's simplify the equation step by step:

First, we'll evaluate the cube and square terms.
(-2/3)^3 = (-2/3)*(-2/3)*(-2/3) = -8/27
(-2/3)^2 = (-2/3)*(-2/3) = 4/9

Now, substitute these values into the equation:
6(-8/27) - 4(4/9) + k(-2/3) - k

Next, simplify the equation further:
-48/27 - 16/9 + k(-2/3) - k

Now, let's find a common denominator to add the fractions:
-48/27 - 16/9 = -16/9 - 16/9 = -32/9

Substituting back into the equation:
-32/9 + k(-2/3) - k

To combine like terms, we can write k as k(1) and simplify it:
-32/9 + k(-2/3) - k(1)

Multiply k by (-2/3):
-32/9 - (2/3)k - k

Now, we'll combine all the terms:
-32/9 - (2/3)k - k

To simplify, let's find a common denominator:
-32/9 - (2/3)k = -32/9 - (6/9)k

Combine the terms with "k":
-32/9 - (6/9)k = -32/9 - 6k/9

To add the fractions, we need a common denominator:
-32/9 - 6k/9 = (-32 - 6k)/9

Now, we have the equation in simplified form:
(-32 - 6k)/9 - k = 0

To solve for "k", we can multiply both sides of the equation by 9:
(-32 - 6k) - 9k = 0

Now, let's solve for "k":
-32 - 6k - 9k = 0

Combine the "k" terms:
-32 - 15k = 0

To isolate "k", add 32 to both sides:
-15k = 32

Divide both sides by -15:
k = 32/(-15)

The value of "k" that satisfies the given condition is:
k = -32/15