70q=-q^2+12000

Solution for 70q=-q^2+12000 equation:

Simplifying
70q = -1q2 + 12000

Reorder the terms:
70q = 12000 + -1q2

Solving
70q = 12000 + -1q2

Solving for variable 'q'.

Reorder the terms:
-12000 + 70q + q2 = 12000 + -1q2 + -12000 + q2

Reorder the terms:
-12000 + 70q + q2 = 12000 + -12000 + -1q2 + q2

Combine like terms: 12000 + -12000 = 0
-12000 + 70q + q2 = 0 + -1q2 + q2
-12000 + 70q + q2 = -1q2 + q2

Combine like terms: -1q2 + q2 = 0
-12000 + 70q + q2 = 0

Factor a trinomial.
(-150 + -1q)(80 + -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 '(80 + -1q)' equal to zero and attempt to solve:

Simplifying
80 + -1q = 0

Solving
80 + -1q = 0

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

Add '-80' to each side of the equation.
80 + -80 + -1q = 0 + -80

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

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

Divide each side by '-1'.
q = 80

Simplifying
q = 80
Solution
q = {-150, 80}