2000=-10000+5000x-500x^2

Solution for 2000=-10000+5000x-500x^2 equation:

Simplifying
2000 = -10000 + 5000x + -500x2

Solving
2000 = -10000 + 5000x + -500x2

Solving for variable 'x'.

Combine like terms: 2000 + 10000 = 12000
12000 + -5000x + 500x2 = -10000 + 5000x + -500x2 + 10000 + -5000x + 500x2

Reorder the terms:
12000 + -5000x + 500x2 = -10000 + 10000 + 5000x + -5000x + -500x2 + 500x2

Combine like terms: -10000 + 10000 = 0
12000 + -5000x + 500x2 = 0 + 5000x + -5000x + -500x2 + 500x2
12000 + -5000x + 500x2 = 5000x + -5000x + -500x2 + 500x2

Combine like terms: 5000x + -5000x = 0
12000 + -5000x + 500x2 = 0 + -500x2 + 500x2
12000 + -5000x + 500x2 = -500x2 + 500x2

Combine like terms: -500x2 + 500x2 = 0
12000 + -5000x + 500x2 = 0

Factor out the Greatest Common Factor (GCF), '500'.
500(24 + -10x + x2) = 0

Factor a trinomial.
500((4 + -1x)(6 + -1x)) = 0

Ignore the factor 500.
Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {4, 6}