-45+24r-3r^2=0

Solution for -45+24r-3r^2=0 equation:

Simplifying
-45 + 24r + -3r2 = 0

Solving
-45 + 24r + -3r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-15 + 8r + -1r2) = 0

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

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

Simplifying
-5 + r = 0

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

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

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

Simplifying
r = 5
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 = {5, 3}