5r^2-23r+24=0

Solution for 5r^2-23r+24=0 equation:

Simplifying
5r2 + -23r + 24 = 0

Reorder the terms:
24 + -23r + 5r2 = 0

Solving
24 + -23r + 5r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(8 + -5r)(3 + -1r) = 0

Subproblem 1
Set the factor '(8 + -5r)' equal to zero and attempt to solve:

Simplifying
8 + -5r = 0

Solving
8 + -5r = 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 + -5r = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -5r = 0 + -8
-5r = 0 + -8

Combine like terms: 0 + -8 = -8
-5r = -8

Divide each side by '-5'.
r = 1.6

Simplifying
r = 1.6
Subproblem 2
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
Solution
r = {1.6, 3}