4r^2-2r-72=0

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

Simplifying
4r2 + -2r + -72 = 0

Reorder the terms:
-72 + -2r + 4r2 = 0

Solving
-72 + -2r + 4r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-36 + -1r + 2r2) = 0

Factor a trinomial.
2((-4 + -1r)(9 + -2r)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-4 + -1r)' equal to zero and attempt to solve:

Simplifying
-4 + -1r = 0

Solving
-4 + -1r = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1r = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1r = 0 + 4
-1r = 0 + 4

Combine like terms: 0 + 4 = 4
-1r = 4

Divide each side by '-1'.
r = -4

Simplifying
r = -4
Subproblem 2
Set the factor '(9 + -2r)' equal to zero and attempt to solve:

Simplifying
9 + -2r = 0

Solving
9 + -2r = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2r = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2r = 0 + -9
-2r = 0 + -9

Combine like terms: 0 + -9 = -9
-2r = -9

Divide each side by '-2'.
r = 4.5

Simplifying
r = 4.5
Solution
r = {-4, 4.5}