1000x-x^2=0

Solution for 1000x-x^2=0 equation:

Simplifying
1000x + -1x2 = 0

Solving
1000x + -1x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(1000 + -1x) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(1000 + -1x)' equal to zero and attempt to solve:

Simplifying
1000 + -1x = 0

Solving
1000 + -1x = 0

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

Add '-1000' to each side of the equation.
1000 + -1000 + -1x = 0 + -1000

Combine like terms: 1000 + -1000 = 0
0 + -1x = 0 + -1000
-1x = 0 + -1000

Combine like terms: 0 + -1000 = -1000
-1x = -1000

Divide each side by '-1'.
x = 1000

Simplifying
x = 1000
Solution
x = {0, 1000}