12r^2s-13rs-35s=0

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Solution for 12r^2s-13rs-35s=0 equation: 


Simplifying
12r2s + -13rs + -35s = 0

Reorder the terms:
-13rs + 12r2s + -35s = 0

Solving
-13rs + 12r2s + -35s = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), 's'.
s(-13r + 12r2 + -35) = 0

Factor a trinomial.
s((3r + -7)(4r + 5)) = 0


Subproblem 1
Set the factor 's' equal to zero and attempt to solve:

Simplifying
s = 0

Solving
s = 0

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

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

Simplifying
0 = -1s

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(3r + -7)' equal to zero and attempt to solve:

Simplifying
3r + -7 = 0

Reorder the terms:
-7 + 3r = 0

Solving
-7 + 3r = 0

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

Add '7' to each side of the equation.
-7 + 7 + 3r = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 3r = 0 + 7
3r = 0 + 7

Combine like terms: 0 + 7 = 7
3r = 7

Divide each side by '3'.
r = 2.333333333

Simplifying
r = 2.333333333

Subproblem 3
Set the factor '(4r + 5)' equal to zero and attempt to solve:

Simplifying
4r + 5 = 0

Reorder the terms:
5 + 4r = 0

Solving
5 + 4r = 0

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

Add '-5' to each side of the equation.
5 + -5 + 4r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4r = 0 + -5
4r = 0 + -5

Combine like terms: 0 + -5 = -5
4r = -5

Divide each side by '4'.
r = -1.25

Simplifying
r = -1.25
Solution
r = {2.333333333, -1.25}

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