-r^2+13r-22=0

Solution for -r^2+13r-22=0 equation:

Simplifying
-1r2 + 13r + -22 = 0

Reorder the terms:
-22 + 13r + -1r2 = 0

Solving
-22 + 13r + -1r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-11 + r)(2 + -1r) = 0

Subproblem 1
Set the factor '(-11 + r)' equal to zero and attempt to solve:

Simplifying
-11 + r = 0

Solving
-11 + r = 0

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

Add '11' to each side of the equation.
-11 + 11 + r = 0 + 11

Combine like terms: -11 + 11 = 0
0 + r = 0 + 11
r = 0 + 11

Combine like terms: 0 + 11 = 11
r = 11

Simplifying
r = 11
Subproblem 2
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
Solution
r = {11, 2}