r^2+7rs+12s^2=0

Solution for r^2+7rs+12s^2=0 equation:

Simplifying
r2 + 7rs + 12s2 = 0

Reorder the terms:
7rs + r2 + 12s2 = 0

Solving
7rs + r2 + 12s2 = 0

Solving for variable 'r'.

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

Subproblem 1
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
Subproblem 2
Set the factor '(r + 4s)' equal to zero and attempt to solve:

Simplifying
r + 4s = 0

Solving
r + 4s = 0

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

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

Combine like terms: 4s + -4s = 0
r + 0 = 0 + -4s
r = 0 + -4s
Remove the zero:
r = -4s

Simplifying
r = -4s
Solution
r = {-3s, -4s}