3r^2-35r+100=0

Solution for 3r^2-35r+100=0 equation:

Simplifying
3r2 + -35r + 100 = 0

Reorder the terms:
100 + -35r + 3r2 = 0

Solving
100 + -35r + 3r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(5 + -1r)(20 + -3r) = 0

Subproblem 1
Set the factor '(5 + -1r)' equal to zero and attempt to solve:

Simplifying
5 + -1r = 0

Solving
5 + -1r = 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 + -1r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1r = 0 + -5
-1r = 0 + -5

Combine like terms: 0 + -5 = -5
-1r = -5

Divide each side by '-1'.
r = 5

Simplifying
r = 5
Subproblem 2
Set the factor '(20 + -3r)' equal to zero and attempt to solve:

Simplifying
20 + -3r = 0

Solving
20 + -3r = 0

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

Add '-20' to each side of the equation.
20 + -20 + -3r = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -3r = 0 + -20
-3r = 0 + -20

Combine like terms: 0 + -20 = -20
-3r = -20

Divide each side by '-3'.
r = 6.666666667

Simplifying
r = 6.666666667
Solution
r = {5, 6.666666667}