2L^2-6L-20=0

Solution for 2L^2-6L-20=0 equation:

Simplifying
2L2 + -6L + -20 = 0

Reorder the terms:
-20 + -6L + 2L2 = 0

Solving
-20 + -6L + 2L2 = 0

Solving for variable 'L'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + -3L + L2) = 0

Factor a trinomial.
2((-2 + -1L)(5 + -1L)) = 0

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

Simplifying
-2 + -1L = 0

Solving
-2 + -1L = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1L = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1L = 0 + 2
-1L = 0 + 2

Combine like terms: 0 + 2 = 2
-1L = 2

Divide each side by '-1'.
L = -2

Simplifying
L = -2
Subproblem 2
Set the factor '(5 + -1L)' equal to zero and attempt to solve:

Simplifying
5 + -1L = 0

Solving
5 + -1L = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1L = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1L = 0 + -5
-1L = 0 + -5

Combine like terms: 0 + -5 = -5
-1L = -5

Divide each side by '-1'.
L = 5

Simplifying
L = 5
Solution
L = {-2, 5}