5v^2=-8v-3

Solution for 5v^2=-8v-3 equation:

Simplifying
5v2 = -8v + -3

Reorder the terms:
5v2 = -3 + -8v

Solving
5v2 = -3 + -8v

Solving for variable 'v'.

Reorder the terms:
3 + 8v + 5v2 = -3 + -8v + 3 + 8v

Reorder the terms:
3 + 8v + 5v2 = -3 + 3 + -8v + 8v

Combine like terms: -3 + 3 = 0
3 + 8v + 5v2 = 0 + -8v + 8v
3 + 8v + 5v2 = -8v + 8v

Combine like terms: -8v + 8v = 0
3 + 8v + 5v2 = 0

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

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

Simplifying
1 + v = 0

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

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

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

Simplifying
v = -1
Subproblem 2
Set the factor '(3 + 5v)' equal to zero and attempt to solve:

Simplifying
3 + 5v = 0

Solving
3 + 5v = 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 + 5v = 0 + -3

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

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

Divide each side by '5'.
v = -0.6

Simplifying
v = -0.6
Solution
v = {-1, -0.6}