r*r+10r+9=0

Solution for r*r+10r+9=0 equation:

Simplifying
r * r + 10r + 9 = 0

Multiply r * r
r2 + 10r + 9 = 0

Reorder the terms:
9 + 10r + r2 = 0

Solving
9 + 10r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(9 + r)(1 + r) = 0

Subproblem 1
Set the factor '(9 + r)' equal to zero and attempt to solve:

Simplifying
9 + r = 0

Solving
9 + r = 0

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

Add '-9' to each side of the equation.
9 + -9 + r = 0 + -9

Combine like terms: 9 + -9 = 0
0 + r = 0 + -9
r = 0 + -9

Combine like terms: 0 + -9 = -9
r = -9

Simplifying
r = -9
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 = {-9, -1}