v^2+3v-1=-3

Solution for v^2+3v-1=-3 equation:

Simplifying
v2 + 3v + -1 = -3

Reorder the terms:
-1 + 3v + v2 = -3

Solving
-1 + 3v + v2 = -3

Solving for variable 'v'.

Reorder the terms:
-1 + 3 + 3v + v2 = -3 + 3

Combine like terms: -1 + 3 = 2
2 + 3v + v2 = -3 + 3

Combine like terms: -3 + 3 = 0
2 + 3v + v2 = 0

Factor a trinomial.
(2 + v)(1 + v) = 0

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

Simplifying
2 + v = 0

Solving
2 + v = 0

Move all terms containing v to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + v = 0 + -2

Combine like terms: 2 + -2 = 0
0 + v = 0 + -2
v = 0 + -2

Combine like terms: 0 + -2 = -2
v = -2

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