(r+6)(r+2)=5

Solution for (r+6)(r+2)=5 equation:

Simplifying
(r + 6)(r + 2) = 5

Reorder the terms:
(6 + r)(r + 2) = 5

Reorder the terms:
(6 + r)(2 + r) = 5

Multiply (6 + r) * (2 + r)
(6(2 + r) + r(2 + r)) = 5
((2 * 6 + r * 6) + r(2 + r)) = 5
((12 + 6r) + r(2 + r)) = 5
(12 + 6r + (2 * r + r * r)) = 5
(12 + 6r + (2r + r2)) = 5

Combine like terms: 6r + 2r = 8r
(12 + 8r + r2) = 5

Solving
12 + 8r + r2 = 5

Solving for variable 'r'.

Reorder the terms:
12 + -5 + 8r + r2 = 5 + -5

Combine like terms: 12 + -5 = 7
7 + 8r + r2 = 5 + -5

Combine like terms: 5 + -5 = 0
7 + 8r + r2 = 0

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

Subproblem 1
Set the factor '(7 + r)' equal to zero and attempt to solve:

Simplifying
7 + r = 0

Solving
7 + r = 0

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

Add '-7' to each side of the equation.
7 + -7 + r = 0 + -7

Combine like terms: 7 + -7 = 0
0 + r = 0 + -7
r = 0 + -7

Combine like terms: 0 + -7 = -7
r = -7

Simplifying
r = -7
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 = {-7, -1}