L(15-L)=54

Solution for L(15-L)=54 equation:

Simplifying
L(15 + -1L) = 54
(15 * L + -1L * L) = 54
(15L + -1L2) = 54

Solving
15L + -1L2 = 54

Solving for variable 'L'.

Reorder the terms:
-54 + 15L + -1L2 = 54 + -54

Combine like terms: 54 + -54 = 0
-54 + 15L + -1L2 = 0

Factor a trinomial.
(-9 + L)(6 + -1L) = 0

Subproblem 1
Set the factor '(-9 + L)' equal to zero and attempt to solve:

Simplifying
-9 + L = 0

Solving
-9 + L = 0

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

Add '9' to each side of the equation.
-9 + 9 + L = 0 + 9

Combine like terms: -9 + 9 = 0
0 + L = 0 + 9
L = 0 + 9

Combine like terms: 0 + 9 = 9
L = 9

Simplifying
L = 9
Subproblem 2
Set the factor '(6 + -1L)' equal to zero and attempt to solve:

Simplifying
6 + -1L = 0

Solving
6 + -1L = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1L = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1L = 0 + -6
-1L = 0 + -6

Combine like terms: 0 + -6 = -6
-1L = -6

Divide each side by '-1'.
L = 6

Simplifying
L = 6
Solution
L = {9, 6}