(r+4)(r+25)=0

Solution for (r+4)(r+25)=0 equation:

Simplifying
(r + 4)(r + 25) = 0

Reorder the terms:
(4 + r)(r + 25) = 0

Reorder the terms:
(4 + r)(25 + r) = 0

Multiply (4 + r) * (25 + r)
(4(25 + r) + r(25 + r)) = 0
((25 * 4 + r * 4) + r(25 + r)) = 0
((100 + 4r) + r(25 + r)) = 0
(100 + 4r + (25 * r + r * r)) = 0
(100 + 4r + (25r + r2)) = 0

Combine like terms: 4r + 25r = 29r
(100 + 29r + r2) = 0

Solving
100 + 29r + r2 = 0

Solving for variable 'r'.

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

Subproblem 1
Set the factor '(25 + r)' equal to zero and attempt to solve:

Simplifying
25 + r = 0

Solving
25 + r = 0

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

Add '-25' to each side of the equation.
25 + -25 + r = 0 + -25

Combine like terms: 25 + -25 = 0
0 + r = 0 + -25
r = 0 + -25

Combine like terms: 0 + -25 = -25
r = -25

Simplifying
r = -25
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 = {-25, -4}