l^2+5l=176

Solution for l^2+5l=176 equation:

Simplifying
l2 + 5l = 176

Reorder the terms:
5l + l2 = 176

Solving
5l + l2 = 176

Solving for variable 'l'.

Reorder the terms:
-176 + 5l + l2 = 176 + -176

Combine like terms: 176 + -176 = 0
-176 + 5l + l2 = 0

Factor a trinomial.
(-16 + -1l)(11 + -1l) = 0

Subproblem 1
Set the factor '(-16 + -1l)' equal to zero and attempt to solve:

Simplifying
-16 + -1l = 0

Solving
-16 + -1l = 0

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

Add '16' to each side of the equation.
-16 + 16 + -1l = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -1l = 0 + 16
-1l = 0 + 16

Combine like terms: 0 + 16 = 16
-1l = 16

Divide each side by '-1'.
l = -16

Simplifying
l = -16
Subproblem 2
Set the factor '(11 + -1l)' equal to zero and attempt to solve:

Simplifying
11 + -1l = 0

Solving
11 + -1l = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1l = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1l = 0 + -11
-1l = 0 + -11

Combine like terms: 0 + -11 = -11
-1l = -11

Divide each side by '-1'.
l = 11

Simplifying
l = 11
Solution
l = {-16, 11}