(8n-1)(n-1)=0

Solution for (8n-1)(n-1)=0 equation:

Simplifying
(8n + -1)(n + -1) = 0

Reorder the terms:
(-1 + 8n)(n + -1) = 0

Reorder the terms:
(-1 + 8n)(-1 + n) = 0

Multiply (-1 + 8n) * (-1 + n)
(-1(-1 + n) + 8n * (-1 + n)) = 0
((-1 * -1 + n * -1) + 8n * (-1 + n)) = 0
((1 + -1n) + 8n * (-1 + n)) = 0
(1 + -1n + (-1 * 8n + n * 8n)) = 0
(1 + -1n + (-8n + 8n2)) = 0

Combine like terms: -1n + -8n = -9n
(1 + -9n + 8n2) = 0

Solving
1 + -9n + 8n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(1 + -8n)(1 + -1n) = 0

Subproblem 1
Set the factor '(1 + -8n)' equal to zero and attempt to solve:

Simplifying
1 + -8n = 0

Solving
1 + -8n = 0

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

Add '-1' to each side of the equation.
1 + -1 + -8n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -8n = 0 + -1
-8n = 0 + -1

Combine like terms: 0 + -1 = -1
-8n = -1

Divide each side by '-8'.
n = 0.125

Simplifying
n = 0.125
Subproblem 2
Set the factor '(1 + -1n)' equal to zero and attempt to solve:

Simplifying
1 + -1n = 0

Solving
1 + -1n = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1n = 0 + -1
-1n = 0 + -1

Combine like terms: 0 + -1 = -1
-1n = -1

Divide each side by '-1'.
n = 1

Simplifying
n = 1
Solution
n = {0.125, 1}