l^2-l-72=0

Solution for l^2-l-72=0 equation:

Simplifying
l2 + -1l + -72 = 0

Reorder the terms:
-72 + -1l + l2 = 0

Solving
-72 + -1l + l2 = 0

Solving for variable 'l'.

Factor a trinomial.
(-8 + -1l)(9 + -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 '(9 + -1l)' equal to zero and attempt to solve:

Simplifying
9 + -1l = 0

Solving
9 + -1l = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1l = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1l = 0 + -9
-1l = 0 + -9

Combine like terms: 0 + -9 = -9
-1l = -9

Divide each side by '-1'.
l = 9

Simplifying
l = 9
Solution
l = {-8, 9}