(r+21)(r-24)=0

Solution for (r+21)(r-24)=0 equation:

Simplifying
(r + 21)(r + -24) = 0

Reorder the terms:
(21 + r)(r + -24) = 0

Reorder the terms:
(21 + r)(-24 + r) = 0

Multiply (21 + r) * (-24 + r)
(21(-24 + r) + r(-24 + r)) = 0
((-24 * 21 + r * 21) + r(-24 + r)) = 0
((-504 + 21r) + r(-24 + r)) = 0
(-504 + 21r + (-24 * r + r * r)) = 0
(-504 + 21r + (-24r + r2)) = 0

Combine like terms: 21r + -24r = -3r
(-504 + -3r + r2) = 0

Solving
-504 + -3r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-21 + -1r)(24 + -1r) = 0

Subproblem 1
Set the factor '(-21 + -1r)' equal to zero and attempt to solve:

Simplifying
-21 + -1r = 0

Solving
-21 + -1r = 0

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

Add '21' to each side of the equation.
-21 + 21 + -1r = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -1r = 0 + 21
-1r = 0 + 21

Combine like terms: 0 + 21 = 21
-1r = 21

Divide each side by '-1'.
r = -21

Simplifying
r = -21
Subproblem 2
Set the factor '(24 + -1r)' equal to zero and attempt to solve:

Simplifying
24 + -1r = 0

Solving
24 + -1r = 0

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

Add '-24' to each side of the equation.
24 + -24 + -1r = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -1r = 0 + -24
-1r = 0 + -24

Combine like terms: 0 + -24 = -24
-1r = -24

Divide each side by '-1'.
r = 24

Simplifying
r = 24
Solution
r = {-21, 24}