2rs-7r+2s-4rs+9r-2s=

Solution for 2rs-7r+2s-4rs+9r-2s= equation:

Simplifying
2rs + -7r + 2s + -4rs + 9r + -2s = 0

Reorder the terms:
-7r + 9r + 2rs + -4rs + 2s + -2s = 0

Combine like terms: -7r + 9r = 2r
2r + 2rs + -4rs + 2s + -2s = 0

Combine like terms: 2rs + -4rs = -2rs
2r + -2rs + 2s + -2s = 0

Combine like terms: 2s + -2s = 0
2r + -2rs + 0 = 0
2r + -2rs = 0

Solving
2r + -2rs = 0

Solving for variable 'r'.

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

Factor out the Greatest Common Factor (GCF), '2r'.
2r(1 + -1s) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'r' equal to zero and attempt to solve:

Simplifying
r = 0

Solving
r = 0

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

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

Simplifying
1 + -1s = 0

Solving
1 + -1s = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1s = 0 + -1
-1s = 0 + -1

Combine like terms: 0 + -1 = -1
-1s = -1

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

Combine like terms: -1s + s = 0
0 = -1 + s

Simplifying
0 = -1 + s

The solution to this equation could not be determined.

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