r^2-22r+21=0

Solution for r^2-22r+21=0 equation:

Simplifying
r2 + -22r + 21 = 0

Reorder the terms:
21 + -22r + r2 = 0

Solving
21 + -22r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(1 + -1r)(21 + -1r) = 0

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

Simplifying
1 + -1r = 0

Solving
1 + -1r = 0

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

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

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

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

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

Simplifying
r = 1
Subproblem 2
Set the factor '(21 + -1r)' equal to zero and attempt to solve:

Simplifying
21 + -1r = 0

Solving
21 + -1r = 0

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

Add '-21' to each side of the equation.
21 + -21 + -1r = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -1r = 0 + -21
-1r = 0 + -21

Combine like terms: 0 + -21 = -21
-1r = -21

Divide each side by '-1'.
r = 21

Simplifying
r = 21
Solution
r = {1, 21}