3v^2=8v+3

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

Simplifying
3v2 = 8v + 3

Reorder the terms:
3v2 = 3 + 8v

Solving
3v2 = 3 + 8v

Solving for variable 'v'.

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

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

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

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

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

Subproblem 1
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
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 = {-0.3333333333, 3}