r^2-36r+180=0

Solution for r^2-36r+180=0 equation:

Simplifying
r2 + -36r + 180 = 0

Reorder the terms:
180 + -36r + r2 = 0

Solving
180 + -36r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(6 + -1r)(30 + -1r) = 0

Subproblem 1
Set the factor '(6 + -1r)' equal to zero and attempt to solve:

Simplifying
6 + -1r = 0

Solving
6 + -1r = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1r = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1r = 0 + -6
-1r = 0 + -6

Combine like terms: 0 + -6 = -6
-1r = -6

Divide each side by '-1'.
r = 6

Simplifying
r = 6
Subproblem 2
Set the factor '(30 + -1r)' equal to zero and attempt to solve:

Simplifying
30 + -1r = 0

Solving
30 + -1r = 0

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

Add '-30' to each side of the equation.
30 + -30 + -1r = 0 + -30

Combine like terms: 30 + -30 = 0
0 + -1r = 0 + -30
-1r = 0 + -30

Combine like terms: 0 + -30 = -30
-1r = -30

Divide each side by '-1'.
r = 30

Simplifying
r = 30
Solution
r = {6, 30}