(l-6)*l=72

Solution for (l-6)*l=72 equation:

Simplifying
(l + -6) * l = 72

Reorder the terms:
(-6 + l) * l = 72

Reorder the terms for easier multiplication:
l(-6 + l) = 72
(-6 * l + l * l) = 72
(-6l + l2) = 72

Solving
-6l + l2 = 72

Solving for variable 'l'.

Reorder the terms:
-72 + -6l + l2 = 72 + -72

Combine like terms: 72 + -72 = 0
-72 + -6l + l2 = 0

Factor a trinomial.
(-6 + -1l)(12 + -1l) = 0

Subproblem 1
Set the factor '(-6 + -1l)' equal to zero and attempt to solve:

Simplifying
-6 + -1l = 0

Solving
-6 + -1l = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1l = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1l = 0 + 6
-1l = 0 + 6

Combine like terms: 0 + 6 = 6
-1l = 6

Divide each side by '-1'.
l = -6

Simplifying
l = -6
Subproblem 2
Set the factor '(12 + -1l)' equal to zero and attempt to solve:

Simplifying
12 + -1l = 0

Solving
12 + -1l = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1l = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1l = 0 + -12
-1l = 0 + -12

Combine like terms: 0 + -12 = -12
-1l = -12

Divide each side by '-1'.
l = 12

Simplifying
l = 12
Solution
l = {-6, 12}