2=3r-r^2

Solution for 2=3r-r^2 equation:

Simplifying
2 = 3r + -1r2

Solving
2 = 3r + -1r2

Solving for variable 'r'.

Reorder the terms:
2 + -3r + r2 = 3r + -3r + -1r2 + r2

Combine like terms: 3r + -3r = 0
2 + -3r + r2 = 0 + -1r2 + r2
2 + -3r + r2 = -1r2 + r2

Combine like terms: -1r2 + r2 = 0
2 + -3r + r2 = 0

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

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

Simplifying
1 + -1r = 0

Solving
1 + -1r = 0

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

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

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

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

Divide each side by '-1'.
r = 1

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

Simplifying
2 + -1r = 0

Solving
2 + -1r = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1r = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1r = 0 + -2
-1r = 0 + -2

Combine like terms: 0 + -2 = -2
-1r = -2

Divide each side by '-1'.
r = 2

Simplifying
r = 2
Solution
r = {1, 2}