3r^2-5rs+2s^2=

Solution for 3r^2-5rs+2s^2= equation:

Simplifying
3r2 + -5rs + 2s2 = 0

Reorder the terms:
-5rs + 3r2 + 2s2 = 0

Solving
-5rs + 3r2 + 2s2 = 0

Solving for variable 'r'.

Factor a trinomial.
(r + -1s)(3r + -2s) = 0

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

Simplifying
r + -1s = 0

Solving
r + -1s = 0

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

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

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

Simplifying
r = s
Subproblem 2
Set the factor '(3r + -2s)' equal to zero and attempt to solve:

Simplifying
3r + -2s = 0

Solving
3r + -2s = 0

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

Add '2s' to each side of the equation.
3r + -2s + 2s = 0 + 2s

Combine like terms: -2s + 2s = 0
3r + 0 = 0 + 2s
3r = 0 + 2s
Remove the zero:
3r = 2s

Divide each side by '3'.
r = 0.6666666667s

Simplifying
r = 0.6666666667s
Solution
r = {s, 0.6666666667s}