20v^2-41vr+20r^2=0

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Solution for 20v^2-41vr+20r^2=0 equation: 


Simplifying
20v2 + -41vr + 20r2 = 0

Reorder the terms:
-41rv + 20r2 + 20v2 = 0

Solving
-41rv + 20r2 + 20v2 = 0

Solving for variable 'r'.

Factor a trinomial.
(4r + -5v)(5r + -4v) = 0


Subproblem 1
Set the factor '(4r + -5v)' equal to zero and attempt to solve:

Simplifying
4r + -5v = 0

Solving
4r + -5v = 0

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

Add '5v' to each side of the equation.
4r + -5v + 5v = 0 + 5v

Combine like terms: -5v + 5v = 0
4r + 0 = 0 + 5v
4r = 0 + 5v
Remove the zero:
4r = 5v

Divide each side by '4'.
r = 1.25v

Simplifying
r = 1.25v

Subproblem 2
Set the factor '(5r + -4v)' equal to zero and attempt to solve:

Simplifying
5r + -4v = 0

Solving
5r + -4v = 0

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

Add '4v' to each side of the equation.
5r + -4v + 4v = 0 + 4v

Combine like terms: -4v + 4v = 0
5r + 0 = 0 + 4v
5r = 0 + 4v
Remove the zero:
5r = 4v

Divide each side by '5'.
r = 0.8v

Simplifying
r = 0.8v
Solution
r = {1.25v, 0.8v}

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