(10r^2)-23r+9=0

Solution for (10r^2)-23r+9=0 equation:

Simplifying
(10r2) + -23r + 9 = 0

Reorder the terms:
9 + -23r + (10r2) = 0

Solving
9 + -23r + (10r2) = 0

Solving for variable 'r'.

Factor a trinomial.
(1 + -2r)(9 + -5r) = 0

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

Simplifying
1 + -2r = 0

Solving
1 + -2r = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2r = 0 + -1
-2r = 0 + -1

Combine like terms: 0 + -1 = -1
-2r = -1

Divide each side by '-2'.
r = 0.5

Simplifying
r = 0.5
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 = {0.5, 1.8}