400=-L^2+50L

Solution for 400=-L^2+50L equation:

Simplifying
400 = -1L2 + 50L

Reorder the terms:
400 = 50L + -1L2

Solving
400 = 50L + -1L2

Solving for variable 'L'.

Reorder the terms:
400 + -50L + L2 = 50L + -50L + -1L2 + L2

Combine like terms: 50L + -50L = 0
400 + -50L + L2 = 0 + -1L2 + L2
400 + -50L + L2 = -1L2 + L2

Combine like terms: -1L2 + L2 = 0
400 + -50L + L2 = 0

Factor a trinomial.
(10 + -1L)(40 + -1L) = 0

Subproblem 1
Set the factor '(10 + -1L)' equal to zero and attempt to solve:

Simplifying
10 + -1L = 0

Solving
10 + -1L = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1L = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1L = 0 + -10
-1L = 0 + -10

Combine like terms: 0 + -10 = -10
-1L = -10

Divide each side by '-1'.
L = 10

Simplifying
L = 10
Subproblem 2
Set the factor '(40 + -1L)' equal to zero and attempt to solve:

Simplifying
40 + -1L = 0

Solving
40 + -1L = 0

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

Add '-40' to each side of the equation.
40 + -40 + -1L = 0 + -40

Combine like terms: 40 + -40 = 0
0 + -1L = 0 + -40
-1L = 0 + -40

Combine like terms: 0 + -40 = -40
-1L = -40

Divide each side by '-1'.
L = 40

Simplifying
L = 40
Solution
L = {10, 40}