r^2-31r+84=0

Solution for r^2-31r+84=0 equation:

Simplifying
r2 + -31r + 84 = 0

Reorder the terms:
84 + -31r + r2 = 0

Solving
84 + -31r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(3 + -1r)(28 + -1r) = 0

Subproblem 1
Set the factor '(3 + -1r)' equal to zero and attempt to solve:

Simplifying
3 + -1r = 0

Solving
3 + -1r = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1r = 0 + -3
-1r = 0 + -3

Combine like terms: 0 + -3 = -3
-1r = -3

Divide each side by '-1'.
r = 3

Simplifying
r = 3
Subproblem 2
Set the factor '(28 + -1r)' equal to zero and attempt to solve:

Simplifying
28 + -1r = 0

Solving
28 + -1r = 0

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

Add '-28' to each side of the equation.
28 + -28 + -1r = 0 + -28

Combine like terms: 28 + -28 = 0
0 + -1r = 0 + -28
-1r = 0 + -28

Combine like terms: 0 + -28 = -28
-1r = -28

Divide each side by '-1'.
r = 28

Simplifying
r = 28
Solution
r = {3, 28}