8v^2-9v+1=0

Solution for 8v^2-9v+1=0 equation:

Simplifying
8v2 + -9v + 1 = 0

Reorder the terms:
1 + -9v + 8v2 = 0

Solving
1 + -9v + 8v2 = 0

Solving for variable 'v'.

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

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

Simplifying
1 + -8v = 0

Solving
1 + -8v = 0

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

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

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

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

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

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

Simplifying
1 + -1v = 0

Solving
1 + -1v = 0

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

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

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

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

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

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