L=L(r+R)

Solution for L=L(r+R) equation:

Simplifying
L = L(r + R)

Reorder the terms:
L = L(R + r)
L = (R * L + r * L)
L = (LR + rL)

Solving
L = LR + rL

Solving for variable 'L'.

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

Add '-1LR' to each side of the equation.
L + -1LR = LR + -1LR + rL

Combine like terms: LR + -1LR = 0
L + -1LR = 0 + rL
L + -1LR = rL

Add '-1rL' to each side of the equation.
L + -1LR + -1rL = rL + -1rL

Combine like terms: rL + -1rL = 0
L + -1LR + -1rL = 0

Factor out the Greatest Common Factor (GCF), 'L'.
L(1 + -1R + -1r) = 0

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

Simplifying
L = 0

Solving
L = 0

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

Simplifying
L = 0
Subproblem 2
Set the factor '(1 + -1R + -1r)' equal to zero and attempt to solve:

Simplifying
1 + -1R + -1r = 0

Solving
1 + -1R + -1r = 0

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

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

Reorder the terms:
1 + -1 + -1R + -1r = 0 + -1

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

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

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

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

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

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

Simplifying
0 = -1 + R + r

The solution to this equation could not be determined.

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