0=k(R^2-r^2)

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Solution for 0=k(R^2-r^2) equation: 


Simplifying
0 = k(R2 + -1r2)
0 = (R2 * k + -1r2 * k)
0 = (kR2 + -1kr2)

Solving
0 = kR2 + -1kr2

Solving for variable 'k'.

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

Add '-1kR2' to each side of the equation.
0 + -1kR2 = kR2 + -1kR2 + -1kr2
Remove the zero:
-1kR2 = kR2 + -1kR2 + -1kr2

Combine like terms: kR2 + -1kR2 = 0
-1kR2 = 0 + -1kr2
-1kR2 = -1kr2

Add 'kr2' to each side of the equation.
-1kR2 + kr2 = -1kr2 + kr2

Combine like terms: -1kr2 + kr2 = 0
-1kR2 + kr2 = 0

Factor out the Greatest Common Factor (GCF), 'k'.
k(-1R2 + r2) = 0

Factor a difference between two squares.
k((R + r)(-1R + r)) = 0


Subproblem 1
Set the factor 'k' equal to zero and attempt to solve:

Simplifying
k = 0

Solving
k = 0

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

Simplifying
k = 0

Subproblem 2
Set the factor '(R + r)' equal to zero and attempt to solve:

Simplifying
R + r = 0

Solving
R + r = 0

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

Add '-1R' to each side of the equation.
R + -1R + r = 0 + -1R

Combine like terms: R + -1R = 0
0 + r = 0 + -1R
r = 0 + -1R
Remove the zero:
r = -1R

Add '-1r' to each side of the equation.
r + -1r = -1R + -1r

Combine like terms: r + -1r = 0
0 = -1R + -1r

Simplifying
0 = -1R + -1r

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 3
Set the factor '(-1R + r)' equal to zero and attempt to solve:

Simplifying
-1R + r = 0

Solving
-1R + r = 0

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

Add 'R' to each side of the equation.
-1R + R + r = 0 + R

Combine like terms: -1R + R = 0
0 + r = 0 + R
r = 0 + R
Remove the zero:
r = R

Add '-1r' to each side of the equation.
r + -1r = R + -1r

Combine like terms: r + -1r = 0
0 = R + -1r

Simplifying
0 = R + -1r

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
k = {0}

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