8v=3v^2-3

Solution for 8v=3v^2-3 equation:

Simplifying
8v = 3v2 + -3

Reorder the terms:
8v = -3 + 3v2

Solving
8v = -3 + 3v2

Solving for variable 'v'.

Reorder the terms:
3 + 8v + -3v2 = -3 + 3v2 + 3 + -3v2

Reorder the terms:
3 + 8v + -3v2 = -3 + 3 + 3v2 + -3v2

Combine like terms: -3 + 3 = 0
3 + 8v + -3v2 = 0 + 3v2 + -3v2
3 + 8v + -3v2 = 3v2 + -3v2

Combine like terms: 3v2 + -3v2 = 0
3 + 8v + -3v2 = 0

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

Simplifying
1 + 3v = 0

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

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

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

Divide each side by '3'.
v = -0.3333333333

Simplifying
v = -0.3333333333
Solution
v = {3, -0.3333333333}