16r^2-72r+80=0

Solution for 16r^2-72r+80=0 equation:

Simplifying
16r2 + -72r + 80 = 0

Reorder the terms:
80 + -72r + 16r2 = 0

Solving
80 + -72r + 16r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '8'.
8(10 + -9r + 2r2) = 0

Factor a trinomial.
8((2 + -1r)(5 + -2r)) = 0

Ignore the factor 8.
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 '(5 + -2r)' equal to zero and attempt to solve:

Simplifying
5 + -2r = 0

Solving
5 + -2r = 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 + -2r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2r = 0 + -5
-2r = 0 + -5

Combine like terms: 0 + -5 = -5
-2r = -5

Divide each side by '-2'.
r = 2.5

Simplifying
r = 2.5
Solution
r = {2, 2.5}