r^2-8r+9=-3

Solution for r^2-8r+9=-3 equation:

Simplifying
r2 + -8r + 9 = -3

Reorder the terms:
9 + -8r + r2 = -3

Solving
9 + -8r + r2 = -3

Solving for variable 'r'.

Reorder the terms:
9 + 3 + -8r + r2 = -3 + 3

Combine like terms: 9 + 3 = 12
12 + -8r + r2 = -3 + 3

Combine like terms: -3 + 3 = 0
12 + -8r + r2 = 0

Factor a trinomial.
(2 + -1r)(6 + -1r) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(6 + -1r)' equal to zero and attempt to solve:

Simplifying
6 + -1r = 0

Solving
6 + -1r = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1r = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1r = 0 + -6
-1r = 0 + -6

Combine like terms: 0 + -6 = -6
-1r = -6

Divide each side by '-1'.
r = 6

Simplifying
r = 6
Solution
r = {2, 6}