l^2-4l=32

Solution for l^2-4l=32 equation:

Simplifying
l2 + -4l = 32

Reorder the terms:
-4l + l2 = 32

Solving
-4l + l2 = 32

Solving for variable 'l'.

Reorder the terms:
-32 + -4l + l2 = 32 + -32

Combine like terms: 32 + -32 = 0
-32 + -4l + l2 = 0

Factor a trinomial.
(-4 + -1l)(8 + -1l) = 0

Subproblem 1
Set the factor '(-4 + -1l)' equal to zero and attempt to solve:

Simplifying
-4 + -1l = 0

Solving
-4 + -1l = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1l = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1l = 0 + 4
-1l = 0 + 4

Combine like terms: 0 + 4 = 4
-1l = 4

Divide each side by '-1'.
l = -4

Simplifying
l = -4
Subproblem 2
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
Solution
l = {-4, 8}