2l^2-6l=20

Solution for 2l^2-6l=20 equation:

Simplifying
2l2 + -6l = 20

Reorder the terms:
-6l + 2l2 = 20

Solving
-6l + 2l2 = 20

Solving for variable 'l'.

Reorder the terms:
-20 + -6l + 2l2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + -6l + 2l2 = 0

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}