L(L-4)=96

Solution for L(L-4)=96 equation:

Simplifying
L(L + -4) = 96

Reorder the terms:
L(-4 + L) = 96
(-4 * L + L * L) = 96
(-4L + L2) = 96

Solving
-4L + L2 = 96

Solving for variable 'L'.

Reorder the terms:
-96 + -4L + L2 = 96 + -96

Combine like terms: 96 + -96 = 0
-96 + -4L + L2 = 0

Factor a trinomial.
(-8 + -1L)(12 + -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 '(12 + -1L)' equal to zero and attempt to solve:

Simplifying
12 + -1L = 0

Solving
12 + -1L = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1L = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1L = 0 + -12
-1L = 0 + -12

Combine like terms: 0 + -12 = -12
-1L = -12

Divide each side by '-1'.
L = 12

Simplifying
L = 12
Solution
L = {-8, 12}