2L^2-14L+24=0

Solution for 2L^2-14L+24=0 equation:

Simplifying
2L2 + -14L + 24 = 0

Reorder the terms:
24 + -14L + 2L2 = 0

Solving
24 + -14L + 2L2 = 0

Solving for variable 'L'.

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + -7L + L2) = 0

Factor a trinomial.
2((3 + -1L)(4 + -1L)) = 0

Ignore the factor 2.
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 '(4 + -1L)' equal to zero and attempt to solve:

Simplifying
4 + -1L = 0

Solving
4 + -1L = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1L = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1L = 0 + -4
-1L = 0 + -4

Combine like terms: 0 + -4 = -4
-1L = -4

Divide each side by '-1'.
L = 4

Simplifying
L = 4
Solution
L = {3, 4}