-3r^2-30r+72=0

Solution for -3r^2-30r+72=0 equation:

Simplifying
-3r2 + -30r + 72 = 0

Reorder the terms:
72 + -30r + -3r2 = 0

Solving
72 + -30r + -3r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3'.
3(24 + -10r + -1r2) = 0

Factor a trinomial.
3((2 + -1r)(12 + r)) = 0

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

Simplifying
2 + -1r = 0

Solving
2 + -1r = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1r = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1r = 0 + -2
-1r = 0 + -2

Combine like terms: 0 + -2 = -2
-1r = -2

Divide each side by '-1'.
r = 2

Simplifying
r = 2
Subproblem 2
Set the factor '(12 + r)' equal to zero and attempt to solve:

Simplifying
12 + r = 0

Solving
12 + r = 0

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

Add '-12' to each side of the equation.
12 + -12 + r = 0 + -12

Combine like terms: 12 + -12 = 0
0 + r = 0 + -12
r = 0 + -12

Combine like terms: 0 + -12 = -12
r = -12

Simplifying
r = -12
Solution
r = {2, -12}