L*(L+2)=48

Solution for L*(L+2)=48 equation:

Simplifying
L(L + 2) = 48

Reorder the terms:
L(2 + L) = 48
(2 * L + L * L) = 48
(2L + L2) = 48

Solving
2L + L2 = 48

Solving for variable 'L'.

Reorder the terms:
-48 + 2L + L2 = 48 + -48

Combine like terms: 48 + -48 = 0
-48 + 2L + L2 = 0

Factor a trinomial.
(-8 + -1L)(6 + -1L) = 0

Subproblem 1
Set the factor '(-8 + -1L)' equal to zero and attempt to solve:

Simplifying
-8 + -1L = 0

Solving
-8 + -1L = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1L = 0 + 8

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

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

Divide each side by '-1'.
L = -8

Simplifying
L = -8
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 = {-8, 6}