3rs-7r+5s-4rs+13r-5s=

Solution for 3rs-7r+5s-4rs+13r-5s= equation:

Simplifying
3rs + -7r + 5s + -4rs + 13r + -5s = 0

Reorder the terms:
-7r + 13r + 3rs + -4rs + 5s + -5s = 0

Combine like terms: -7r + 13r = 6r
6r + 3rs + -4rs + 5s + -5s = 0

Combine like terms: 3rs + -4rs = -1rs
6r + -1rs + 5s + -5s = 0

Combine like terms: 5s + -5s = 0
6r + -1rs + 0 = 0
6r + -1rs = 0

Solving
6r + -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(6 + -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 '(6 + -1s)' equal to zero and attempt to solve:

Simplifying
6 + -1s = 0

Solving
6 + -1s = 0

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

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

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

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

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

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

Simplifying
0 = -6 + 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}