l^2+5l=24

Solution for l^2+5l=24 equation:

Simplifying
l2 + 5l = 24

Reorder the terms:
5l + l2 = 24

Solving
5l + l2 = 24

Solving for variable 'l'.

Reorder the terms:
-24 + 5l + l2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + 5l + l2 = 0

Factor a trinomial.
(-8 + -1l)(3 + -1l) = 0

Subproblem 1
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
Subproblem 2
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
Solution
l = {-8, 3}