(1-k)r^2+2kLr-kL^2=0

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Solution for (1-k)r^2+2kLr-kL^2=0 equation: 


Simplifying
(1 + -1k) * r2 + 2kLr + -1kL2 = 0

Reorder the terms for easier multiplication:
r2(1 + -1k) + 2kLr + -1kL2 = 0
(1 * r2 + -1k * r2) + 2kLr + -1kL2 = 0

Reorder the terms:
(-1kr2 + 1r2) + 2kLr + -1kL2 = 0
(-1kr2 + 1r2) + 2kLr + -1kL2 = 0

Reorder the terms:
-1kL2 + 2krL + -1kr2 + 1r2 = 0

Solving
-1kL2 + 2krL + -1kr2 + 1r2 = 0

Solving for variable 'k'.

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

Add '-1r2' to each side of the equation.
-1kL2 + 2krL + -1kr2 + 1r2 + -1r2 = 0 + -1r2

Combine like terms: 1r2 + -1r2 = 0
-1kL2 + 2krL + -1kr2 + 0 = 0 + -1r2
-1kL2 + 2krL + -1kr2 = 0 + -1r2
Remove the zero:
-1kL2 + 2krL + -1kr2 = -1r2

Combine like terms: -1r2 + r2 = 0
-1kL2 + 2krL + -1kr2 + r2 = 0

The solution to this equation could not be determined.

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