(r+1)(r+7)=0

Solution for (r+1)(r+7)=0 equation:

Simplifying
(r + 1)(r + 7) = 0

Reorder the terms:
(1 + r)(r + 7) = 0

Reorder the terms:
(1 + r)(7 + r) = 0

Multiply (1 + r) * (7 + r)
(1(7 + r) + r(7 + r)) = 0
((7 * 1 + r * 1) + r(7 + r)) = 0
((7 + 1r) + r(7 + r)) = 0
(7 + 1r + (7 * r + r * r)) = 0
(7 + 1r + (7r + r2)) = 0

Combine like terms: 1r + 7r = 8r
(7 + 8r + r2) = 0

Solving
7 + 8r + r2 = 0

Solving for variable 'r'.

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}