l(l+2)=168

Solution for l(l+2)=168 equation:

Simplifying
l(l + 2) = 168

Reorder the terms:
l(2 + l) = 168
(2 * l + l * l) = 168
(2l + l2) = 168

Solving
2l + l2 = 168

Solving for variable 'l'.

Reorder the terms:
-168 + 2l + l2 = 168 + -168

Combine like terms: 168 + -168 = 0
-168 + 2l + l2 = 0

Factor a trinomial.
(-14 + -1l)(12 + -1l) = 0

Subproblem 1
Set the factor '(-14 + -1l)' equal to zero and attempt to solve:

Simplifying
-14 + -1l = 0

Solving
-14 + -1l = 0

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

Add '14' to each side of the equation.
-14 + 14 + -1l = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -1l = 0 + 14
-1l = 0 + 14

Combine like terms: 0 + 14 = 14
-1l = 14

Divide each side by '-1'.
l = -14

Simplifying
l = -14
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 = {-14, 12}