v^2=4v-3

Solution for v^2=4v-3 equation:

Simplifying
v2 = 4v + -3

Reorder the terms:
v2 = -3 + 4v

Solving
v2 = -3 + 4v

Solving for variable 'v'.

Reorder the terms:
3 + -4v + v2 = -3 + 4v + 3 + -4v

Reorder the terms:
3 + -4v + v2 = -3 + 3 + 4v + -4v

Combine like terms: -3 + 3 = 0
3 + -4v + v2 = 0 + 4v + -4v
3 + -4v + v2 = 4v + -4v

Combine like terms: 4v + -4v = 0
3 + -4v + v2 = 0

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

Subproblem 1
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
Subproblem 2
Set the factor '(3 + -1v)' equal to zero and attempt to solve:

Simplifying
3 + -1v = 0

Solving
3 + -1v = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1v = 0 + -3

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

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

Divide each side by '-1'.
v = 3

Simplifying
v = 3
Solution
v = {1, 3}