x^2-4kx-32k^2=0

Solution for x^2-4kx-32k^2=0 equation:

Simplifying
x2 + -4kx + -32k2 = 0

Reorder the terms:
-4kx + -32k2 + x2 = 0

Solving
-4kx + -32k2 + x2 = 0

Solving for variable 'k'.

Factor a trinomial.
(-4k + -1x)(8k + -1x) = 0

Subproblem 1
Set the factor '(-4k + -1x)' equal to zero and attempt to solve:

Simplifying
-4k + -1x = 0

Solving
-4k + -1x = 0

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

Add 'x' to each side of the equation.
-4k + -1x + x = 0 + x

Combine like terms: -1x + x = 0
-4k + 0 = 0 + x
-4k = 0 + x
Remove the zero:
-4k = x

Divide each side by '-4'.
k = -0.25x

Simplifying
k = -0.25x
Subproblem 2
Set the factor '(8k + -1x)' equal to zero and attempt to solve:

Simplifying
8k + -1x = 0

Solving
8k + -1x = 0

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

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

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

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

Simplifying
k = 0.125x
Solution
k = {-0.25x, 0.125x}