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.
(21 + r)(1 + r) = 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 + r)' equal to zero and attempt to solve:

Simplifying
1 + r = 0

Solving
1 + r = 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 + r = 0 + -1

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

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

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