x^2+2Kx-3K^2=0

Solution for x^2+2Kx-3K^2=0 equation:

Simplifying
x2 + 2Kx + -3K2 = 0

Reorder the terms:
-3K2 + 2xK + x2 = 0

Solving
-3K2 + 2xK + x2 = 0

Solving for variable 'K'.

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

Subproblem 1
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
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 = {-0.3333333333x, x}