40q=-q^2+6000

Solution for 40q=-q^2+6000 equation:

Simplifying
40q = -1q2 + 6000

Reorder the terms:
40q = 6000 + -1q2

Solving
40q = 6000 + -1q2

Solving for variable 'q'.

Reorder the terms:
-6000 + 40q + q2 = 6000 + -1q2 + -6000 + q2

Reorder the terms:
-6000 + 40q + q2 = 6000 + -6000 + -1q2 + q2

Combine like terms: 6000 + -6000 = 0
-6000 + 40q + q2 = 0 + -1q2 + q2
-6000 + 40q + q2 = -1q2 + q2

Combine like terms: -1q2 + q2 = 0
-6000 + 40q + q2 = 0

Factor a trinomial.
(-100 + -1q)(60 + -1q) = 0

Subproblem 1
Set the factor '(-100 + -1q)' equal to zero and attempt to solve:

Simplifying
-100 + -1q = 0

Solving
-100 + -1q = 0

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

Add '100' to each side of the equation.
-100 + 100 + -1q = 0 + 100

Combine like terms: -100 + 100 = 0
0 + -1q = 0 + 100
-1q = 0 + 100

Combine like terms: 0 + 100 = 100
-1q = 100

Divide each side by '-1'.
q = -100

Simplifying
q = -100
Subproblem 2
Set the factor '(60 + -1q)' equal to zero and attempt to solve:

Simplifying
60 + -1q = 0

Solving
60 + -1q = 0

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

Add '-60' to each side of the equation.
60 + -60 + -1q = 0 + -60

Combine like terms: 60 + -60 = 0
0 + -1q = 0 + -60
-1q = 0 + -60

Combine like terms: 0 + -60 = -60
-1q = -60

Divide each side by '-1'.
q = 60

Simplifying
q = 60
Solution
q = {-100, 60}