12r^2-64r+80=0

Solution for 12r^2-64r+80=0 equation:

Simplifying
12r2 + -64r + 80 = 0

Reorder the terms:
80 + -64r + 12r2 = 0

Solving
80 + -64r + 12r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '4'.
4(20 + -16r + 3r2) = 0

Factor a trinomial.
4((2 + -1r)(10 + -3r)) = 0

Ignore the factor 4.
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 '(10 + -3r)' equal to zero and attempt to solve:

Simplifying
10 + -3r = 0

Solving
10 + -3r = 0

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

Add '-10' to each side of the equation.
10 + -10 + -3r = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -3r = 0 + -10
-3r = 0 + -10

Combine like terms: 0 + -10 = -10
-3r = -10

Divide each side by '-3'.
r = 3.333333333

Simplifying
r = 3.333333333
Solution
r = {2, 3.333333333}