(r+1)(r+4)=0

Solution for (r+1)(r+4)=0 equation:

Simplifying
(r + 1)(r + 4) = 0

Reorder the terms:
(1 + r)(r + 4) = 0

Reorder the terms:
(1 + r)(4 + r) = 0

Multiply (1 + r) * (4 + r)
(1(4 + r) + r(4 + r)) = 0
((4 * 1 + r * 1) + r(4 + r)) = 0
((4 + 1r) + r(4 + r)) = 0
(4 + 1r + (4 * r + r * r)) = 0
(4 + 1r + (4r + r2)) = 0

Combine like terms: 1r + 4r = 5r
(4 + 5r + r2) = 0

Solving
4 + 5r + r2 = 0

Solving for variable 'r'.

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

Subproblem 1
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
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 = {-4, -1}