r^2=9r-20

Solution for r^2=9r-20 equation:

Simplifying
r2 = 9r + -20

Reorder the terms:
r2 = -20 + 9r

Solving
r2 = -20 + 9r

Solving for variable 'r'.

Reorder the terms:
20 + -9r + r2 = -20 + 9r + 20 + -9r

Reorder the terms:
20 + -9r + r2 = -20 + 20 + 9r + -9r

Combine like terms: -20 + 20 = 0
20 + -9r + r2 = 0 + 9r + -9r
20 + -9r + r2 = 9r + -9r

Combine like terms: 9r + -9r = 0
20 + -9r + r2 = 0

Factor a trinomial.
(4 + -1r)(5 + -1r) = 0

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

Simplifying
4 + -1r = 0

Solving
4 + -1r = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1r = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1r = 0 + -4
-1r = 0 + -4

Combine like terms: 0 + -4 = -4
-1r = -4

Divide each side by '-1'.
r = 4

Simplifying
r = 4
Subproblem 2
Set the factor '(5 + -1r)' equal to zero and attempt to solve:

Simplifying
5 + -1r = 0

Solving
5 + -1r = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1r = 0 + -5
-1r = 0 + -5

Combine like terms: 0 + -5 = -5
-1r = -5

Divide each side by '-1'.
r = 5

Simplifying
r = 5
Solution
r = {4, 5}