4v-3=v^2

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

Simplifying
4v + -3 = v2

Reorder the terms:
-3 + 4v = v2

Solving
-3 + 4v = v2

Solving for variable 'v'.

Combine like terms: v2 + -1v2 = 0
-3 + 4v + -1v2 = 0

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

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

Simplifying
-3 + v = 0

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

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

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

Simplifying
v = 3
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 = {3, 1}