r^2=6r-9

Solution for r^2=6r-9 equation:

Simplifying
r2 = 6r + -9

Reorder the terms:
r2 = -9 + 6r

Solving
r2 = -9 + 6r

Solving for variable 'r'.

Reorder the terms:
9 + -6r + r2 = -9 + 6r + 9 + -6r

Reorder the terms:
9 + -6r + r2 = -9 + 9 + 6r + -6r

Combine like terms: -9 + 9 = 0
9 + -6r + r2 = 0 + 6r + -6r
9 + -6r + r2 = 6r + -6r

Combine like terms: 6r + -6r = 0
9 + -6r + r2 = 0

Factor a trinomial.
(3 + -1r)(3 + -1r) = 0

Subproblem 1
Set the factor '(3 + -1r)' equal to zero and attempt to solve:

Simplifying
3 + -1r = 0

Solving
3 + -1r = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1r = 0 + -3

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

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

Divide each side by '-1'.
r = 3

Simplifying
r = 3
Subproblem 2
Set the factor '(3 + -1r)' equal to zero and attempt to solve:

Simplifying
3 + -1r = 0

Solving
3 + -1r = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1r = 0 + -3

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

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

Divide each side by '-1'.
r = 3

Simplifying
r = 3
Solution
r = {3, 3}