3r^2-17rs-6s^2=

Solution for 3r^2-17rs-6s^2= equation:

Simplifying
3r2 + -17rs + -6s2 = 0

Reorder the terms:
-17rs + 3r2 + -6s2 = 0

Solving
-17rs + 3r2 + -6s2 = 0

Solving for variable 'r'.

Factor a trinomial.
(r + -6s)(3r + s) = 0

Subproblem 1
Set the factor '(r + -6s)' equal to zero and attempt to solve:

Simplifying
r + -6s = 0

Solving
r + -6s = 0

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

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

Combine like terms: -6s + 6s = 0
r + 0 = 0 + 6s
r = 0 + 6s
Remove the zero:
r = 6s

Simplifying
r = 6s
Subproblem 2
Set the factor '(3r + s)' equal to zero and attempt to solve:

Simplifying
3r + s = 0

Solving
3r + s = 0

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

Add '-1s' to each side of the equation.
3r + s + -1s = 0 + -1s

Combine like terms: s + -1s = 0
3r + 0 = 0 + -1s
3r = 0 + -1s
Remove the zero:
3r = -1s

Divide each side by '3'.
r = -0.3333333333s

Simplifying
r = -0.3333333333s
Solution
r = {6s, -0.3333333333s}