2L^2-28L+96=0

Solution for 2L^2-28L+96=0 equation:

Simplifying
2L2 + -28L + 96 = 0

Reorder the terms:
96 + -28L + 2L2 = 0

Solving
96 + -28L + 2L2 = 0

Solving for variable 'L'.

Factor out the Greatest Common Factor (GCF), '2'.
2(48 + -14L + L2) = 0

Factor a trinomial.
2((6 + -1L)(8 + -1L)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
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
Solution
L = {6, 8}