3r^2-34r+80=0

Solution for 3r^2-34r+80=0 equation:

Simplifying
3r2 + -34r + 80 = 0

Reorder the terms:
80 + -34r + 3r2 = 0

Solving
80 + -34r + 3r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(10 + -3r)(8 + -1r) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(8 + -1r)' equal to zero and attempt to solve:

Simplifying
8 + -1r = 0

Solving
8 + -1r = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1r = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1r = 0 + -8
-1r = 0 + -8

Combine like terms: 0 + -8 = -8
-1r = -8

Divide each side by '-1'.
r = 8

Simplifying
r = 8
Solution
r = {3.333333333, 8}