2r^2+12rs-32s^2=0

Solution for 2r^2+12rs-32s^2=0 equation:

Simplifying
2r2 + 12rs + -32s2 = 0

Reorder the terms:
12rs + 2r2 + -32s2 = 0

Solving
12rs + 2r2 + -32s2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6rs + r2 + -16s2) = 0

Factor a trinomial.
2((r + -2s)(r + 8s)) = 0

Ignore the factor 2.
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 + 8s)' equal to zero and attempt to solve:

Simplifying
r + 8s = 0

Solving
r + 8s = 0

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

Add '-8s' to each side of the equation.
r + 8s + -8s = 0 + -8s

Combine like terms: 8s + -8s = 0
r + 0 = 0 + -8s
r = 0 + -8s
Remove the zero:
r = -8s

Simplifying
r = -8s
Solution
r = {2s, -8s}