l^2-13l=-40

Solution for l^2-13l=-40 equation:

Simplifying
l2 + -13l = -40

Reorder the terms:
-13l + l2 = -40

Solving
-13l + l2 = -40

Solving for variable 'l'.

Reorder the terms:
40 + -13l + l2 = -40 + 40

Combine like terms: -40 + 40 = 0
40 + -13l + l2 = 0

Factor a trinomial.
(5 + -1l)(8 + -1l) = 0

Subproblem 1
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
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 = {5, 8}