9v^2-12v+3=0

Solution for 9v^2-12v+3=0 equation:

Simplifying
9v2 + -12v + 3 = 0

Reorder the terms:
3 + -12v + 9v2 = 0

Solving
3 + -12v + 9v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + -4v + 3v2) = 0

Factor a trinomial.
3((1 + -3v)(1 + -1v)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(1 + -3v)' equal to zero and attempt to solve:

Simplifying
1 + -3v = 0

Solving
1 + -3v = 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 + -3v = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3v = 0 + -1
-3v = 0 + -1

Combine like terms: 0 + -1 = -1
-3v = -1

Divide each side by '-3'.
v = 0.3333333333

Simplifying
v = 0.3333333333
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 = {0.3333333333, 1}