(r-25)(r+49)=0

Solution for (r-25)(r+49)=0 equation:

Simplifying
(r + -25)(r + 49) = 0

Reorder the terms:
(-25 + r)(r + 49) = 0

Reorder the terms:
(-25 + r)(49 + r) = 0

Multiply (-25 + r) * (49 + r)
(-25(49 + r) + r(49 + r)) = 0
((49 * -25 + r * -25) + r(49 + r)) = 0
((-1225 + -25r) + r(49 + r)) = 0
(-1225 + -25r + (49 * r + r * r)) = 0
(-1225 + -25r + (49r + r2)) = 0

Combine like terms: -25r + 49r = 24r
(-1225 + 24r + r2) = 0

Solving
-1225 + 24r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-49 + -1r)(25 + -1r) = 0

Subproblem 1
Set the factor '(-49 + -1r)' equal to zero and attempt to solve:

Simplifying
-49 + -1r = 0

Solving
-49 + -1r = 0

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

Add '49' to each side of the equation.
-49 + 49 + -1r = 0 + 49

Combine like terms: -49 + 49 = 0
0 + -1r = 0 + 49
-1r = 0 + 49

Combine like terms: 0 + 49 = 49
-1r = 49

Divide each side by '-1'.
r = -49

Simplifying
r = -49
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 = {-49, 25}