v^2-3v^2+3v-1=0

Solution for v^2-3v^2+3v-1=0 equation:

Simplifying
v2 + -3v2 + 3v + -1 = 0

Reorder the terms:
-1 + 3v + v2 + -3v2 = 0

Combine like terms: v2 + -3v2 = -2v2
-1 + 3v + -2v2 = 0

Solving
-1 + 3v + -2v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(-1 + v)(1 + -2v) = 0

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

Simplifying
-1 + v = 0

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

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

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

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

Simplifying
1 + -2v = 0

Solving
1 + -2v = 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 + -2v = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2v = 0 + -1
-2v = 0 + -1

Combine like terms: 0 + -1 = -1
-2v = -1

Divide each side by '-2'.
v = 0.5

Simplifying
v = 0.5
Solution
v = {1, 0.5}