X(2r-1000)=0

Solution for X(2r-1000)=0 equation:

Simplifying
X(2r + -1000) = 0

Reorder the terms:
X(-1000 + 2r) = 0
(-1000 * X + 2r * X) = 0
(-1000X + 2rX) = 0

Solving
-1000X + 2rX = 0

Solving for variable 'X'.

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

Factor out the Greatest Common Factor (GCF), '2X'.
2X(-500 + r) = 0

Ignore the factor 2.
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 '(-500 + r)' equal to zero and attempt to solve:

Simplifying
-500 + r = 0

Solving
-500 + r = 0

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

Add '500' to each side of the equation.
-500 + 500 + r = 0 + 500

Combine like terms: -500 + 500 = 0
0 + r = 0 + 500
r = 0 + 500

Combine like terms: 0 + 500 = 500
r = 500

Add '-1r' to each side of the equation.
r + -1r = 500 + -1r

Combine like terms: r + -1r = 0
0 = 500 + -1r

Simplifying
0 = 500 + -1r

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
X = {0}