8r^2-2r-1=0

Solution for 8r^2-2r-1=0 equation:

Simplifying
8r2 + -2r + -1 = 0

Reorder the terms:
-1 + -2r + 8r2 = 0

Solving
-1 + -2r + 8r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-1 + -4r)(1 + -2r) = 0

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

Simplifying
-1 + -4r = 0

Solving
-1 + -4r = 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 + -4r = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4r = 0 + 1
-4r = 0 + 1

Combine like terms: 0 + 1 = 1
-4r = 1

Divide each side by '-4'.
r = -0.25

Simplifying
r = -0.25
Subproblem 2
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
Solution
r = {-0.25, 0.5}