20r^2-39r+18=0

Solution for 20r^2-39r+18=0 equation:

Simplifying
20r2 + -39r + 18 = 0

Reorder the terms:
18 + -39r + 20r2 = 0

Solving
18 + -39r + 20r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(3 + -4r)(6 + -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 '(6 + -5r)' equal to zero and attempt to solve:

Simplifying
6 + -5r = 0

Solving
6 + -5r = 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 + -5r = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5r = 0 + -6
-5r = 0 + -6

Combine like terms: 0 + -6 = -6
-5r = -6

Divide each side by '-5'.
r = 1.2

Simplifying
r = 1.2
Solution
r = {0.75, 1.2}