r^2-21r+54=0

Solution for r^2-21r+54=0 equation:

Simplifying
r2 + -21r + 54 = 0

Reorder the terms:
54 + -21r + r2 = 0

Solving
54 + -21r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(3 + -1r)(18 + -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 '(18 + -1r)' equal to zero and attempt to solve:

Simplifying
18 + -1r = 0

Solving
18 + -1r = 0

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

Add '-18' to each side of the equation.
18 + -18 + -1r = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -1r = 0 + -18
-1r = 0 + -18

Combine like terms: 0 + -18 = -18
-1r = -18

Divide each side by '-1'.
r = 18

Simplifying
r = 18
Solution
r = {3, 18}