-4r^2-12rs-8s^2=

Solution for -4r^2-12rs-8s^2= equation:

Simplifying
-4r2 + -12rs + -8s2 = 0

Reorder the terms:
-12rs + -4r2 + -8s2 = 0

Solving
-12rs + -4r2 + -8s2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '-4'.
-4(3rs + r2 + 2s2) = 0

Factor a trinomial.
-4((r + s)(r + 2s)) = 0

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

Simplifying
r + s = 0

Solving
r + s = 0

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

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

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

Simplifying
r = -1s
Subproblem 2
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
Solution
r = {-1s, -2s}