16r^2-18r+5=0

Solution for 16r^2-18r+5=0 equation:

Simplifying
16r2 + -18r + 5 = 0

Reorder the terms:
5 + -18r + 16r2 = 0

Solving
5 + -18r + 16r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(1 + -2r)(5 + -8r) = 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 '(5 + -8r)' equal to zero and attempt to solve:

Simplifying
5 + -8r = 0

Solving
5 + -8r = 0

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

Add '-5' to each side of the equation.
5 + -5 + -8r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -8r = 0 + -5
-8r = 0 + -5

Combine like terms: 0 + -5 = -5
-8r = -5

Divide each side by '-8'.
r = 0.625

Simplifying
r = 0.625
Solution
r = {0.5, 0.625}