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

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

Simplifying
3k2 + -1x2 + -2xk = 0

Reorder the terms:
-2kx + 3k2 + -1x2 = 0

Solving
-2kx + 3k2 + -1x2 = 0

Solving for variable 'k'.

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

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

Simplifying
3k + x = 0

Solving
3k + x = 0

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

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

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

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

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