x^2+kx-2k^2=0

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

Simplifying
x2 + kx + -2k2 = 0

Reorder the terms:
kx + -2k2 + x2 = 0

Solving
kx + -2k2 + x2 = 0

Solving for variable 'k'.

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

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

Simplifying
-2k + -1x = 0

Solving
-2k + -1x = 0

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

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

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

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

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

Simplifying
k + -1x = 0

Solving
k + -1x = 0

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

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

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

Simplifying
k = x
Solution
k = {-0.5x, x}