r^2-20rs-44s^2=0

Solution for r^2-20rs-44s^2=0 equation:

Simplifying
r2 + -20rs + -44s2 = 0

Reorder the terms:
-20rs + r2 + -44s2 = 0

Solving
-20rs + r2 + -44s2 = 0

Solving for variable 'r'.

Factor a trinomial.
(r + -22s)(r + 2s) = 0

Subproblem 1
Set the factor '(r + -22s)' equal to zero and attempt to solve:

Simplifying
r + -22s = 0

Solving
r + -22s = 0

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

Add '22s' to each side of the equation.
r + -22s + 22s = 0 + 22s

Combine like terms: -22s + 22s = 0
r + 0 = 0 + 22s
r = 0 + 22s
Remove the zero:
r = 22s

Simplifying
r = 22s
Subproblem 2
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
Solution
r = {22s, -2s}