(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 = 21r
(-100 + 21r + r2) = 0

Solving
-100 + 21r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-25 + -1r)(4 + -1r) = 0

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

Simplifying
-25 + -1r = 0

Solving
-25 + -1r = 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 + -1r = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -1r = 0 + 25
-1r = 0 + 25

Combine like terms: 0 + 25 = 25
-1r = 25

Divide each side by '-1'.
r = -25

Simplifying
r = -25
Subproblem 2
Set the factor '(4 + -1r)' equal to zero and attempt to solve:

Simplifying
4 + -1r = 0

Solving
4 + -1r = 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 + -1r = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1r = 0 + -4
-1r = 0 + -4

Combine like terms: 0 + -4 = -4
-1r = -4

Divide each side by '-1'.
r = 4

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