0=l^2-45l-9000

Solution for 0=l^2-45l-9000 equation:

Simplifying
0 = l2 + -45l + -9000

Reorder the terms:
0 = -9000 + -45l + l2

Solving
0 = -9000 + -45l + l2

Solving for variable 'l'.

Combine like terms: 0 + 9000 = 9000
9000 + 45l + -1l2 = -9000 + -45l + l2 + 9000 + 45l + -1l2

Reorder the terms:
9000 + 45l + -1l2 = -9000 + 9000 + -45l + 45l + l2 + -1l2

Combine like terms: -9000 + 9000 = 0
9000 + 45l + -1l2 = 0 + -45l + 45l + l2 + -1l2
9000 + 45l + -1l2 = -45l + 45l + l2 + -1l2

Combine like terms: -45l + 45l = 0
9000 + 45l + -1l2 = 0 + l2 + -1l2
9000 + 45l + -1l2 = l2 + -1l2

Combine like terms: l2 + -1l2 = 0
9000 + 45l + -1l2 = 0

Factor a trinomial.
(120 + -1l)(75 + l) = 0

Subproblem 1
Set the factor '(120 + -1l)' equal to zero and attempt to solve:

Simplifying
120 + -1l = 0

Solving
120 + -1l = 0

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

Add '-120' to each side of the equation.
120 + -120 + -1l = 0 + -120

Combine like terms: 120 + -120 = 0
0 + -1l = 0 + -120
-1l = 0 + -120

Combine like terms: 0 + -120 = -120
-1l = -120

Divide each side by '-1'.
l = 120

Simplifying
l = 120
Subproblem 2
Set the factor '(75 + l)' equal to zero and attempt to solve:

Simplifying
75 + l = 0

Solving
75 + l = 0

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

Add '-75' to each side of the equation.
75 + -75 + l = 0 + -75

Combine like terms: 75 + -75 = 0
0 + l = 0 + -75
l = 0 + -75

Combine like terms: 0 + -75 = -75
l = -75

Simplifying
l = -75
Solution
l = {120, -75}