r^2-8r+11=-4

Solution for r^2-8r+11=-4 equation:

Simplifying
r2 + -8r + 11 = -4

Reorder the terms:
11 + -8r + r2 = -4

Solving
11 + -8r + r2 = -4

Solving for variable 'r'.

Reorder the terms:
11 + 4 + -8r + r2 = -4 + 4

Combine like terms: 11 + 4 = 15
15 + -8r + r2 = -4 + 4

Combine like terms: -4 + 4 = 0
15 + -8r + r2 = 0

Factor a trinomial.
(3 + -1r)(5 + -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 '(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 = {3, 5}