15=L(8-L)

Solution for 15=L(8-L) equation:

Simplifying
15 = L(8 + -1L)
15 = (8 * L + -1L * L)
15 = (8L + -1L2)

Solving
15 = 8L + -1L2

Solving for variable 'L'.

Reorder the terms:
15 + -8L + L2 = 8L + -8L + -1L2 + L2

Combine like terms: 8L + -8L = 0
15 + -8L + L2 = 0 + -1L2 + L2
15 + -8L + L2 = -1L2 + L2

Combine like terms: -1L2 + L2 = 0
15 + -8L + L2 = 0

Factor a trinomial.
(3 + -1L)(5 + -1L) = 0

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

Simplifying
3 + -1L = 0

Solving
3 + -1L = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1L = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1L = 0 + -3
-1L = 0 + -3

Combine like terms: 0 + -3 = -3
-1L = -3

Divide each side by '-1'.
L = 3

Simplifying
L = 3
Subproblem 2
Set the factor '(5 + -1L)' equal to zero and attempt to solve:

Simplifying
5 + -1L = 0

Solving
5 + -1L = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1L = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1L = 0 + -5
-1L = 0 + -5

Combine like terms: 0 + -5 = -5
-1L = -5

Divide each side by '-1'.
L = 5

Simplifying
L = 5
Solution
L = {3, 5}