r^2+20r+61=-3

Solution for r^2+20r+61=-3 equation:

Simplifying
r2 + 20r + 61 = -3

Reorder the terms:
61 + 20r + r2 = -3

Solving
61 + 20r + r2 = -3

Solving for variable 'r'.

Reorder the terms:
61 + 3 + 20r + r2 = -3 + 3

Combine like terms: 61 + 3 = 64
64 + 20r + r2 = -3 + 3

Combine like terms: -3 + 3 = 0
64 + 20r + r2 = 0

Factor a trinomial.
(16 + r)(4 + r) = 0

Subproblem 1
Set the factor '(16 + r)' equal to zero and attempt to solve:

Simplifying
16 + r = 0

Solving
16 + r = 0

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

Add '-16' to each side of the equation.
16 + -16 + r = 0 + -16

Combine like terms: 16 + -16 = 0
0 + r = 0 + -16
r = 0 + -16

Combine like terms: 0 + -16 = -16
r = -16

Simplifying
r = -16
Subproblem 2
Set the factor '(4 + r)' equal to zero and attempt to solve:

Simplifying
4 + r = 0

Solving
4 + r = 0

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

Add '-4' to each side of the equation.
4 + -4 + r = 0 + -4

Combine like terms: 4 + -4 = 0
0 + r = 0 + -4
r = 0 + -4

Combine like terms: 0 + -4 = -4
r = -4

Simplifying
r = -4
Solution
r = {-16, -4}