(r-25)(r+64)=0

Solution for (r-25)(r+64)=0 equation:

Simplifying
(r + -25)(r + 64) = 0

Reorder the terms:
(-25 + r)(r + 64) = 0

Reorder the terms:
(-25 + r)(64 + r) = 0

Multiply (-25 + r) * (64 + r)
(-25(64 + r) + r(64 + r)) = 0
((64 * -25 + r * -25) + r(64 + r)) = 0
((-1600 + -25r) + r(64 + r)) = 0
(-1600 + -25r + (64 * r + r * r)) = 0
(-1600 + -25r + (64r + r2)) = 0

Combine like terms: -25r + 64r = 39r
(-1600 + 39r + r2) = 0

Solving
-1600 + 39r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-64 + -1r)(25 + -1r) = 0

Subproblem 1
Set the factor '(-64 + -1r)' equal to zero and attempt to solve:

Simplifying
-64 + -1r = 0

Solving
-64 + -1r = 0

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

Add '64' to each side of the equation.
-64 + 64 + -1r = 0 + 64

Combine like terms: -64 + 64 = 0
0 + -1r = 0 + 64
-1r = 0 + 64

Combine like terms: 0 + 64 = 64
-1r = 64

Divide each side by '-1'.
r = -64

Simplifying
r = -64
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 = {-64, 25}