28r^2-53r+24=0

Solution for 28r^2-53r+24=0 equation:

Simplifying
28r2 + -53r + 24 = 0

Reorder the terms:
24 + -53r + 28r2 = 0

Solving
24 + -53r + 28r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(3 + -4r)(8 + -7r) = 0

Subproblem 1
Set the factor '(3 + -4r)' equal to zero and attempt to solve:

Simplifying
3 + -4r = 0

Solving
3 + -4r = 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 + -4r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4r = 0 + -3
-4r = 0 + -3

Combine like terms: 0 + -3 = -3
-4r = -3

Divide each side by '-4'.
r = 0.75

Simplifying
r = 0.75
Subproblem 2
Set the factor '(8 + -7r)' equal to zero and attempt to solve:

Simplifying
8 + -7r = 0

Solving
8 + -7r = 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 + -7r = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -7r = 0 + -8
-7r = 0 + -8

Combine like terms: 0 + -8 = -8
-7r = -8

Divide each side by '-7'.
r = 1.142857143

Simplifying
r = 1.142857143
Solution
r = {0.75, 1.142857143}