l^2-6l=91

Solution for l^2-6l=91 equation:

Simplifying
l2 + -6l = 91

Reorder the terms:
-6l + l2 = 91

Solving
-6l + l2 = 91

Solving for variable 'l'.

Reorder the terms:
-91 + -6l + l2 = 91 + -91

Combine like terms: 91 + -91 = 0
-91 + -6l + l2 = 0

Factor a trinomial.
(-7 + -1l)(13 + -1l) = 0

Subproblem 1
Set the factor '(-7 + -1l)' equal to zero and attempt to solve:

Simplifying
-7 + -1l = 0

Solving
-7 + -1l = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1l = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1l = 0 + 7
-1l = 0 + 7

Combine like terms: 0 + 7 = 7
-1l = 7

Divide each side by '-1'.
l = -7

Simplifying
l = -7
Subproblem 2
Set the factor '(13 + -1l)' equal to zero and attempt to solve:

Simplifying
13 + -1l = 0

Solving
13 + -1l = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1l = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1l = 0 + -13
-1l = 0 + -13

Combine like terms: 0 + -13 = -13
-1l = -13

Divide each side by '-1'.
l = 13

Simplifying
l = 13
Solution
l = {-7, 13}