5v^2-2v-3=0

Solution for 5v^2-2v-3=0 equation:

Simplifying
5v2 + -2v + -3 = 0

Reorder the terms:
-3 + -2v + 5v2 = 0

Solving
-3 + -2v + 5v2 = 0

Solving for variable 'v'.

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

Subproblem 1
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
Subproblem 2
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
Solution
v = {-0.6, 1}