5r^2-11rs+2s^2=0

Solution for 5r^2-11rs+2s^2=0 equation:

Simplifying
5r2 + -11rs + 2s2 = 0

Reorder the terms:
-11rs + 5r2 + 2s2 = 0

Solving
-11rs + 5r2 + 2s2 = 0

Solving for variable 'r'.

Factor a trinomial.
(r + -2s)(5r + -1s) = 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 '(5r + -1s)' equal to zero and attempt to solve:

Simplifying
5r + -1s = 0

Solving
5r + -1s = 0

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

Add 's' to each side of the equation.
5r + -1s + s = 0 + s

Combine like terms: -1s + s = 0
5r + 0 = 0 + s
5r = 0 + s
Remove the zero:
5r = s

Divide each side by '5'.
r = 0.2s

Simplifying
r = 0.2s
Solution
r = {2s, 0.2s}