4v^2=-v+3

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

Simplifying
4v2 = -1v + 3

Reorder the terms:
4v2 = 3 + -1v

Solving
4v2 = 3 + -1v

Solving for variable 'v'.

Reorder the terms:
-3 + v + 4v2 = 3 + -1v + -3 + v

Reorder the terms:
-3 + v + 4v2 = 3 + -3 + -1v + v

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

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

Factor a trinomial.
(-1 + -1v)(3 + -4v) = 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 + -4v)' equal to zero and attempt to solve:

Simplifying
3 + -4v = 0

Solving
3 + -4v = 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 + -4v = 0 + -3

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

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

Divide each side by '-4'.
v = 0.75

Simplifying
v = 0.75
Solution
v = {-1, 0.75}