-4r^2+72r+576=0

Solution for -4r^2+72r+576=0 equation:

Simplifying
-4r2 + 72r + 576 = 0

Reorder the terms:
576 + 72r + -4r2 = 0

Solving
576 + 72r + -4r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '4'.
4(144 + 18r + -1r2) = 0

Factor a trinomial.
4((24 + -1r)(6 + r)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(24 + -1r)' equal to zero and attempt to solve:

Simplifying
24 + -1r = 0

Solving
24 + -1r = 0

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

Add '-24' to each side of the equation.
24 + -24 + -1r = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -1r = 0 + -24
-1r = 0 + -24

Combine like terms: 0 + -24 = -24
-1r = -24

Divide each side by '-1'.
r = 24

Simplifying
r = 24
Subproblem 2
Set the factor '(6 + r)' equal to zero and attempt to solve:

Simplifying
6 + r = 0

Solving
6 + r = 0

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

Add '-6' to each side of the equation.
6 + -6 + r = 0 + -6

Combine like terms: 6 + -6 = 0
0 + r = 0 + -6
r = 0 + -6

Combine like terms: 0 + -6 = -6
r = -6

Simplifying
r = -6
Solution
r = {24, -6}