L^2-15L=54

Solution for L^2-15L=54 equation:

Simplifying
L2 + -15L = 54

Reorder the terms:
-15L + L2 = 54

Solving
-15L + L2 = 54

Solving for variable 'L'.

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

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

Factor a trinomial.
(-3 + -1L)(18 + -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 '(18 + -1L)' equal to zero and attempt to solve:

Simplifying
18 + -1L = 0

Solving
18 + -1L = 0

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

Add '-18' to each side of the equation.
18 + -18 + -1L = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -1L = 0 + -18
-1L = 0 + -18

Combine like terms: 0 + -18 = -18
-1L = -18

Divide each side by '-1'.
L = 18

Simplifying
L = 18
Solution
L = {-3, 18}