90q=-q^2+9000

Solution for 90q=-q^2+9000 equation:

Simplifying
90q = -1q2 + 9000

Reorder the terms:
90q = 9000 + -1q2

Solving
90q = 9000 + -1q2

Solving for variable 'q'.

Reorder the terms:
-9000 + 90q + q2 = 9000 + -1q2 + -9000 + q2

Reorder the terms:
-9000 + 90q + q2 = 9000 + -9000 + -1q2 + q2

Combine like terms: 9000 + -9000 = 0
-9000 + 90q + q2 = 0 + -1q2 + q2
-9000 + 90q + q2 = -1q2 + q2

Combine like terms: -1q2 + q2 = 0
-9000 + 90q + q2 = 0

Factor a trinomial.
(-150 + -1q)(60 + -1q) = 0

Subproblem 1
Set the factor '(-150 + -1q)' equal to zero and attempt to solve:

Simplifying
-150 + -1q = 0

Solving
-150 + -1q = 0

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

Add '150' to each side of the equation.
-150 + 150 + -1q = 0 + 150

Combine like terms: -150 + 150 = 0
0 + -1q = 0 + 150
-1q = 0 + 150

Combine like terms: 0 + 150 = 150
-1q = 150

Divide each side by '-1'.
q = -150

Simplifying
q = -150
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 = {-150, 60}