L(L-45)=9000

Solution for L(L-45)=9000 equation:

Simplifying
L(L + -45) = 9000

Reorder the terms:
L(-45 + L) = 9000
(-45 * L + L * L) = 9000
(-45L + L2) = 9000

Solving
-45L + L2 = 9000

Solving for variable 'L'.

Reorder the terms:
-9000 + -45L + L2 = 9000 + -9000

Combine like terms: 9000 + -9000 = 0
-9000 + -45L + L2 = 0

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

Subproblem 1
Set the factor '(-75 + -1L)' equal to zero and attempt to solve:

Simplifying
-75 + -1L = 0

Solving
-75 + -1L = 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 + -1L = 0 + 75

Combine like terms: -75 + 75 = 0
0 + -1L = 0 + 75
-1L = 0 + 75

Combine like terms: 0 + 75 = 75
-1L = 75

Divide each side by '-1'.
L = -75

Simplifying
L = -75
Subproblem 2
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
Solution
L = {-75, 120}