27r^2-66rs+24s^2=0

Solution for 27r^2-66rs+24s^2=0 equation:

Simplifying
27r2 + -66rs + 24s2 = 0

Reorder the terms:
-66rs + 27r2 + 24s2 = 0

Solving
-66rs + 27r2 + 24s2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-22rs + 9r2 + 8s2) = 0

Factor a trinomial.
3((r + -2s)(9r + -4s)) = 0

Ignore the factor 3.
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 '(9r + -4s)' equal to zero and attempt to solve:

Simplifying
9r + -4s = 0

Solving
9r + -4s = 0

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

Add '4s' to each side of the equation.
9r + -4s + 4s = 0 + 4s

Combine like terms: -4s + 4s = 0
9r + 0 = 0 + 4s
9r = 0 + 4s
Remove the zero:
9r = 4s

Divide each side by '9'.
r = 0.4444444444s

Simplifying
r = 0.4444444444s
Solution
r = {2s, 0.4444444444s}