r^2+5rs+6s^2=0

Solution for r^2+5rs+6s^2=0 equation:

Simplifying
r2 + 5rs + 6s2 = 0

Reorder the terms:
5rs + r2 + 6s2 = 0

Solving
5rs + r2 + 6s2 = 0

Solving for variable 'r'.

Factor a trinomial.
(r + 2s)(r + 3s) = 0

Subproblem 1
Set the factor '(r + 2s)' equal to zero and attempt to solve:

Simplifying
r + 2s = 0

Solving
r + 2s = 0

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

Add '-2s' to each side of the equation.
r + 2s + -2s = 0 + -2s

Combine like terms: 2s + -2s = 0
r + 0 = 0 + -2s
r = 0 + -2s
Remove the zero:
r = -2s

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

Simplifying
r + 3s = 0

Solving
r + 3s = 0

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

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

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

Simplifying
r = -3s
Solution
r = {-2s, -3s}