z^2-6zk-16k^2=0

Solution for z^2-6zk-16k^2=0 equation:

Simplifying
z2 + -6zk + -16k2 = 0

Reorder the terms:
-6kz + -16k2 + z2 = 0

Solving
-6kz + -16k2 + z2 = 0

Solving for variable 'k'.

Factor a trinomial.
(-2k + -1z)(8k + -1z) = 0

Subproblem 1
Set the factor '(-2k + -1z)' equal to zero and attempt to solve:

Simplifying
-2k + -1z = 0

Solving
-2k + -1z = 0

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

Add 'z' to each side of the equation.
-2k + -1z + z = 0 + z

Combine like terms: -1z + z = 0
-2k + 0 = 0 + z
-2k = 0 + z
Remove the zero:
-2k = z

Divide each side by '-2'.
k = -0.5z

Simplifying
k = -0.5z
Subproblem 2
Set the factor '(8k + -1z)' equal to zero and attempt to solve:

Simplifying
8k + -1z = 0

Solving
8k + -1z = 0

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

Add 'z' to each side of the equation.
8k + -1z + z = 0 + z

Combine like terms: -1z + z = 0
8k + 0 = 0 + z
8k = 0 + z
Remove the zero:
8k = z

Divide each side by '8'.
k = 0.125z

Simplifying
k = 0.125z
Solution
k = {-0.5z, 0.125z}