r=3.1416(r^2+rs)

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Solution for r=3.1416(r^2+rs) equation: 


Simplifying
r = 3.1416(r2 + rs)

Reorder the terms:
r = 3.1416(rs + r2)
r = (rs * 3.1416 + r2 * 3.1416)
r = (3.1416rs + 3.1416r2)

Solving
r = 3.1416rs + 3.1416r2

Solving for variable 'r'.

Reorder the terms:
r + -3.1416rs + -3.1416r2 = 3.1416rs + -3.1416rs + 3.1416r2 + -3.1416r2

Combine like terms: 3.1416rs + -3.1416rs = 0.0000
r + -3.1416rs + -3.1416r2 = 0.0000 + 3.1416r2 + -3.1416r2
r + -3.1416rs + -3.1416r2 = 3.1416r2 + -3.1416r2

Combine like terms: 3.1416r2 + -3.1416r2 = 0.0000
r + -3.1416rs + -3.1416r2 = 0.0000

Factor out the Greatest Common Factor (GCF), 'r'.
r(1 + -3.1416s + -3.1416r) = 0.0000


Subproblem 1
Set the factor 'r' equal to zero and attempt to solve:

Simplifying
r = 0

Solving
r = 0

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

Simplifying
r = 0

Subproblem 2
Set the factor '(1 + -3.1416s + -3.1416r)' equal to zero and attempt to solve:

Simplifying
1 + -3.1416s + -3.1416r = 0

Reorder the terms:
1 + -3.1416r + -3.1416s = 0

Solving
1 + -3.1416r + -3.1416s = 0

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

Add '-1' to each side of the equation.
1 + -3.1416r + -1 + -3.1416s = 0 + -1

Reorder the terms:
1 + -1 + -3.1416r + -3.1416s = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3.1416r + -3.1416s = 0 + -1
-3.1416r + -3.1416s = 0 + -1

Combine like terms: 0 + -1 = -1
-3.1416r + -3.1416s = -1

Add '3.1416s' to each side of the equation.
-3.1416r + -3.1416s + 3.1416s = -1 + 3.1416s

Combine like terms: -3.1416s + 3.1416s = 0.0000
-3.1416r + 0.0000 = -1 + 3.1416s
-3.1416r = -1 + 3.1416s

Divide each side by '-3.1416'.
r = 0.3183091418 + -1s

Simplifying
r = 0.3183091418 + -1s
Solution
r = {0, 0.3183091418 + -1s}

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