r(r-5)=24

Solution for r(r-5)=24 equation:

Simplifying
r(r + -5) = 24

Reorder the terms:
r(-5 + r) = 24
(-5 * r + r * r) = 24
(-5r + r2) = 24

Solving
-5r + r2 = 24

Solving for variable 'r'.

Reorder the terms:
-24 + -5r + r2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + -5r + r2 = 0

Factor a trinomial.
(-3 + -1r)(8 + -1r) = 0

Subproblem 1
Set the factor '(-3 + -1r)' equal to zero and attempt to solve:

Simplifying
-3 + -1r = 0

Solving
-3 + -1r = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1r = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1r = 0 + 3
-1r = 0 + 3

Combine like terms: 0 + 3 = 3
-1r = 3

Divide each side by '-1'.
r = -3

Simplifying
r = -3
Subproblem 2
Set the factor '(8 + -1r)' equal to zero and attempt to solve:

Simplifying
8 + -1r = 0

Solving
8 + -1r = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1r = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1r = 0 + -8
-1r = 0 + -8

Combine like terms: 0 + -8 = -8
-1r = -8

Divide each side by '-1'.
r = 8

Simplifying
r = 8
Solution
r = {-3, 8}