80q=-q^2+10500

Solution for 80q=-q^2+10500 equation:

Simplifying
80q = -1q2 + 10500

Reorder the terms:
80q = 10500 + -1q2

Solving
80q = 10500 + -1q2

Solving for variable 'q'.

Reorder the terms:
-10500 + 80q + q2 = 10500 + -1q2 + -10500 + q2

Reorder the terms:
-10500 + 80q + q2 = 10500 + -10500 + -1q2 + q2

Combine like terms: 10500 + -10500 = 0
-10500 + 80q + q2 = 0 + -1q2 + q2
-10500 + 80q + q2 = -1q2 + q2

Combine like terms: -1q2 + q2 = 0
-10500 + 80q + q2 = 0

Factor a trinomial.
(-150 + -1q)(70 + -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 '(70 + -1q)' equal to zero and attempt to solve:

Simplifying
70 + -1q = 0

Solving
70 + -1q = 0

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

Add '-70' to each side of the equation.
70 + -70 + -1q = 0 + -70

Combine like terms: 70 + -70 = 0
0 + -1q = 0 + -70
-1q = 0 + -70

Combine like terms: 0 + -70 = -70
-1q = -70

Divide each side by '-1'.
q = 70

Simplifying
q = 70
Solution
q = {-150, 70}