5r(3s)+6r-2rs=

Solution for 5r(3s)+6r-2rs= equation:

Simplifying
5r(3s) + 6r + -2rs = 0

Remove parenthesis around (3s)
5r * 3s + 6r + -2rs = 0

Reorder the terms for easier multiplication:
5 * 3r * s + 6r + -2rs = 0

Multiply 5 * 3
15r * s + 6r + -2rs = 0

Multiply r * s
15rs + 6r + -2rs = 0

Reorder the terms:
6r + 15rs + -2rs = 0

Combine like terms: 15rs + -2rs = 13rs
6r + 13rs = 0

Solving
6r + 13rs = 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 + 13s) = 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 + 13s)' equal to zero and attempt to solve:

Simplifying
6 + 13s = 0

Solving
6 + 13s = 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 + 13s = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 13s = 0 + -6
13s = 0 + -6

Combine like terms: 0 + -6 = -6
13s = -6

Add '-13s' to each side of the equation.
13s + -13s = -6 + -13s

Combine like terms: 13s + -13s = 0
0 = -6 + -13s

Simplifying
0 = -6 + -13s

The solution to this equation could not be determined.

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