=r^2-22r+21

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

Simplifying
0 = r2 + -22r + 21

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

Solving
0 = 21 + -22r + r2

Solving for variable 'r'.

Combine like terms: 0 + -21 = -21
-21 + 22r + -1r2 = 21 + -22r + r2 + -21 + 22r + -1r2

Reorder the terms:
-21 + 22r + -1r2 = 21 + -21 + -22r + 22r + r2 + -1r2

Combine like terms: 21 + -21 = 0
-21 + 22r + -1r2 = 0 + -22r + 22r + r2 + -1r2
-21 + 22r + -1r2 = -22r + 22r + r2 + -1r2

Combine like terms: -22r + 22r = 0
-21 + 22r + -1r2 = 0 + r2 + -1r2
-21 + 22r + -1r2 = r2 + -1r2

Combine like terms: r2 + -1r2 = 0
-21 + 22r + -1r2 = 0

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

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

Simplifying
-21 + r = 0

Solving
-21 + r = 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 + r = 0 + 21

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

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

Simplifying
r = 21
Subproblem 2
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
Solution
r = {21, 1}