14v=5v^2-3

Solution for 14v=5v^2-3 equation:

Simplifying
14v = 5v2 + -3

Reorder the terms:
14v = -3 + 5v2

Solving
14v = -3 + 5v2

Solving for variable 'v'.

Reorder the terms:
3 + 14v + -5v2 = -3 + 5v2 + 3 + -5v2

Reorder the terms:
3 + 14v + -5v2 = -3 + 3 + 5v2 + -5v2

Combine like terms: -3 + 3 = 0
3 + 14v + -5v2 = 0 + 5v2 + -5v2
3 + 14v + -5v2 = 5v2 + -5v2

Combine like terms: 5v2 + -5v2 = 0
3 + 14v + -5v2 = 0

Factor a trinomial.
(3 + -1v)(1 + 5v) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(1 + 5v)' equal to zero and attempt to solve:

Simplifying
1 + 5v = 0

Solving
1 + 5v = 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 + 5v = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5v = 0 + -1
5v = 0 + -1

Combine like terms: 0 + -1 = -1
5v = -1

Divide each side by '5'.
v = -0.2

Simplifying
v = -0.2
Solution
v = {3, -0.2}