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

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

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

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

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

Solving for variable 'r'.

Factor a trinomial.
(2r + -5s)(r + s) = 0

Subproblem 1
Set the factor '(2r + -5s)' equal to zero and attempt to solve:

Simplifying
2r + -5s = 0

Solving
2r + -5s = 0

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

Add '5s' to each side of the equation.
2r + -5s + 5s = 0 + 5s

Combine like terms: -5s + 5s = 0
2r + 0 = 0 + 5s
2r = 0 + 5s
Remove the zero:
2r = 5s

Divide each side by '2'.
r = 2.5s

Simplifying
r = 2.5s
Subproblem 2
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
Solution
r = {2.5s, -1s}