2rs-9r+2s-3rs+10r-2s=

Solution for 2rs-9r+2s-3rs+10r-2s= equation:

Simplifying
2rs + -9r + 2s + -3rs + 10r + -2s = 0

Reorder the terms:
-9r + 10r + 2rs + -3rs + 2s + -2s = 0

Combine like terms: -9r + 10r = 1r
1r + 2rs + -3rs + 2s + -2s = 0

Combine like terms: 2rs + -3rs = -1rs
1r + -1rs + 2s + -2s = 0

Combine like terms: 2s + -2s = 0
1r + -1rs + 0 = 0
1r + -1rs = 0

Solving
1r + -1rs = 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), 'r'.
r(1 + -1s) = 0

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}