(r-25)(r+81)=0

Solution for (r-25)(r+81)=0 equation:

Simplifying
(r + -25)(r + 81) = 0

Reorder the terms:
(-25 + r)(r + 81) = 0

Reorder the terms:
(-25 + r)(81 + r) = 0

Multiply (-25 + r) * (81 + r)
(-25(81 + r) + r(81 + r)) = 0
((81 * -25 + r * -25) + r(81 + r)) = 0
((-2025 + -25r) + r(81 + r)) = 0
(-2025 + -25r + (81 * r + r * r)) = 0
(-2025 + -25r + (81r + r2)) = 0

Combine like terms: -25r + 81r = 56r
(-2025 + 56r + r2) = 0

Solving
-2025 + 56r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-81 + -1r)(25 + -1r) = 0

Subproblem 1
Set the factor '(-81 + -1r)' equal to zero and attempt to solve:

Simplifying
-81 + -1r = 0

Solving
-81 + -1r = 0

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

Add '81' to each side of the equation.
-81 + 81 + -1r = 0 + 81

Combine like terms: -81 + 81 = 0
0 + -1r = 0 + 81
-1r = 0 + 81

Combine like terms: 0 + 81 = 81
-1r = 81

Divide each side by '-1'.
r = -81

Simplifying
r = -81
Subproblem 2
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
Solution
r = {-81, 25}