24r^2-6r-45=0

Solution for 24r^2-6r-45=0 equation:

Simplifying
24r2 + -6r + -45 = 0

Reorder the terms:
-45 + -6r + 24r2 = 0

Solving
-45 + -6r + 24r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-15 + -2r + 8r2) = 0

Factor a trinomial.
3((-5 + -4r)(3 + -2r)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-5 + -4r)' equal to zero and attempt to solve:

Simplifying
-5 + -4r = 0

Solving
-5 + -4r = 0

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

Add '5' to each side of the equation.
-5 + 5 + -4r = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -4r = 0 + 5
-4r = 0 + 5

Combine like terms: 0 + 5 = 5
-4r = 5

Divide each side by '-4'.
r = -1.25

Simplifying
r = -1.25
Subproblem 2
Set the factor '(3 + -2r)' equal to zero and attempt to solve:

Simplifying
3 + -2r = 0

Solving
3 + -2r = 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 + -2r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2r = 0 + -3
-2r = 0 + -3

Combine like terms: 0 + -3 = -3
-2r = -3

Divide each side by '-2'.
r = 1.5

Simplifying
r = 1.5
Solution
r = {-1.25, 1.5}