16r^2-8r=-1

Solution for 16r^2-8r=-1 equation:

Simplifying
16r2 + -8r = -1

Reorder the terms:
-8r + 16r2 = -1

Solving
-8r + 16r2 = -1

Solving for variable 'r'.

Reorder the terms:
1 + -8r + 16r2 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + -8r + 16r2 = 0

Factor a trinomial.
(1 + -4r)(1 + -4r) = 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 + -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
Solution
r = {0.25, 0.25}