r^2+20r+61=10

Solution for r^2+20r+61=10 equation:

Simplifying
r2 + 20r + 61 = 10

Reorder the terms:
61 + 20r + r2 = 10

Solving
61 + 20r + r2 = 10

Solving for variable 'r'.

Reorder the terms:
61 + -10 + 20r + r2 = 10 + -10

Combine like terms: 61 + -10 = 51
51 + 20r + r2 = 10 + -10

Combine like terms: 10 + -10 = 0
51 + 20r + r2 = 0

Factor a trinomial.
(17 + r)(3 + r) = 0

Subproblem 1
Set the factor '(17 + r)' equal to zero and attempt to solve:

Simplifying
17 + r = 0

Solving
17 + r = 0

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

Add '-17' to each side of the equation.
17 + -17 + r = 0 + -17

Combine like terms: 17 + -17 = 0
0 + r = 0 + -17
r = 0 + -17

Combine like terms: 0 + -17 = -17
r = -17

Simplifying
r = -17
Subproblem 2
Set the factor '(3 + r)' equal to zero and attempt to solve:

Simplifying
3 + r = 0

Solving
3 + r = 0

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

Add '-3' to each side of the equation.
3 + -3 + r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + r = 0 + -3
r = 0 + -3

Combine like terms: 0 + -3 = -3
r = -3

Simplifying
r = -3
Solution
r = {-17, -3}