16r^2-8r+1=1

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

Simplifying
16r2 + -8r + 1 = 1

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

Add '-1' to each side of the equation.
1 + -8r + -1 + 16r2 = 1 + -1

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

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

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

Solving
-8r + 16r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '8r'.
8r(-1 + 2r) = 0

Ignore the factor 8.
Subproblem 1
Set the factor 'r' equal to zero and attempt to solve:

Simplifying
r = 0

Solving
r = 0

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

Simplifying
r = 0
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, 0.5}