r^2-9r+11=-3

Solution for r^2-9r+11=-3 equation:

Simplifying
r2 + -9r + 11 = -3

Reorder the terms:
11 + -9r + r2 = -3

Solving
11 + -9r + r2 = -3

Solving for variable 'r'.

Reorder the terms:
11 + 3 + -9r + r2 = -3 + 3

Combine like terms: 11 + 3 = 14
14 + -9r + r2 = -3 + 3

Combine like terms: -3 + 3 = 0
14 + -9r + r2 = 0

Factor a trinomial.
(2 + -1r)(7 + -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 '(7 + -1r)' equal to zero and attempt to solve:

Simplifying
7 + -1r = 0

Solving
7 + -1r = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1r = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1r = 0 + -7
-1r = 0 + -7

Combine like terms: 0 + -7 = -7
-1r = -7

Divide each side by '-1'.
r = 7

Simplifying
r = 7
Solution
r = {2, 7}