x^2-2kx-3k^2=0

Solution for x^2-2kx-3k^2=0 equation:

Simplifying
x2 + -2kx + -3k2 = 0

Reorder the terms:
-2kx + -3k2 + x2 = 0

Solving
-2kx + -3k2 + x2 = 0

Solving for variable 'k'.

Factor a trinomial.
(-1k + -1x)(3k + -1x) = 0

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

Simplifying
-1k + -1x = 0

Solving
-1k + -1x = 0

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

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

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

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

Simplifying
k = -1x
Subproblem 2
Set the factor '(3k + -1x)' equal to zero and attempt to solve:

Simplifying
3k + -1x = 0

Solving
3k + -1x = 0

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

Add 'x' to each side of the equation.
3k + -1x + x = 0 + x

Combine like terms: -1x + x = 0
3k + 0 = 0 + x
3k = 0 + x
Remove the zero:
3k = x

Divide each side by '3'.
k = 0.3333333333x

Simplifying
k = 0.3333333333x
Solution
k = {-1x, 0.3333333333x}