L(23-L)=23

Solution for L(23-L)=23 equation:

Simplifying
L(23 + -1L) = 23
(23 * L + -1L * L) = 23
(23L + -1L2) = 23

Solving
23L + -1L2 = 23

Solving for variable 'L'.

Reorder the terms:
-23 + 23L + -1L2 = 23 + -23

Combine like terms: 23 + -23 = 0
-23 + 23L + -1L2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
23 + -23L + L2 = 0

Move the constant term to the right:

Add '-23' to each side of the equation.
23 + -23L + -23 + L2 = 0 + -23

Reorder the terms:
23 + -23 + -23L + L2 = 0 + -23

Combine like terms: 23 + -23 = 0
0 + -23L + L2 = 0 + -23
-23L + L2 = 0 + -23

Combine like terms: 0 + -23 = -23
-23L + L2 = -23

The L term is -23L.  Take half its coefficient (-11.5).
Square it (132.25) and add it to both sides.

Add '132.25' to each side of the equation.
-23L + 132.25 + L2 = -23 + 132.25

Reorder the terms:
132.25 + -23L + L2 = -23 + 132.25

Combine like terms: -23 + 132.25 = 109.25
132.25 + -23L + L2 = 109.25

Factor a perfect square on the left side:
(L + -11.5)(L + -11.5) = 109.25

Calculate the square root of the right side: 10.45227248

Break this problem into two subproblems by setting 
(L + -11.5) equal to 10.45227248 and -10.45227248.

Subproblem 1
L + -11.5 = 10.45227248

Simplifying
L + -11.5 = 10.45227248

Reorder the terms:
-11.5 + L = 10.45227248

Solving
-11.5 + L = 10.45227248

Solving for variable 'L'.

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

Add '11.5' to each side of the equation.
-11.5 + 11.5 + L = 10.45227248 + 11.5

Combine like terms: -11.5 + 11.5 = 0.0
0.0 + L = 10.45227248 + 11.5
L = 10.45227248 + 11.5

Combine like terms: 10.45227248 + 11.5 = 21.95227248
L = 21.95227248

Simplifying
L = 21.95227248

Subproblem 2
L + -11.5 = -10.45227248

Simplifying
L + -11.5 = -10.45227248

Reorder the terms:
-11.5 + L = -10.45227248

Solving
-11.5 + L = -10.45227248

Solving for variable 'L'.

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

Add '11.5' to each side of the equation.
-11.5 + 11.5 + L = -10.45227248 + 11.5

Combine like terms: -11.5 + 11.5 = 0.0
0.0 + L = -10.45227248 + 11.5
L = -10.45227248 + 11.5

Combine like terms: -10.45227248 + 11.5 = 1.04772752
L = 1.04772752

Simplifying
L = 1.04772752

Solution
The solution to the problem is based on the solutions
from the subproblems.
L = {21.95227248, 1.04772752}