20r^2-51r+27=0

Solution for 20r^2-51r+27=0 equation:

Simplifying
20r2 + -51r + 27 = 0

Reorder the terms:
27 + -51r + 20r2 = 0

Solving
27 + -51r + 20r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(3 + -4r)(9 + -5r) = 0

Subproblem 1
Set the factor '(3 + -4r)' equal to zero and attempt to solve:

Simplifying
3 + -4r = 0

Solving
3 + -4r = 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 + -4r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4r = 0 + -3
-4r = 0 + -3

Combine like terms: 0 + -3 = -3
-4r = -3

Divide each side by '-4'.
r = 0.75

Simplifying
r = 0.75
Subproblem 2
Set the factor '(9 + -5r)' equal to zero and attempt to solve:

Simplifying
9 + -5r = 0

Solving
9 + -5r = 0

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

Add '-9' to each side of the equation.
9 + -9 + -5r = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -5r = 0 + -9
-5r = 0 + -9

Combine like terms: 0 + -9 = -9
-5r = -9

Divide each side by '-5'.
r = 1.8

Simplifying
r = 1.8
Solution
r = {0.75, 1.8}