v^2+3v-46=-6

Solution for v^2+3v-46=-6 equation:

Simplifying
v2 + 3v + -46 = -6

Reorder the terms:
-46 + 3v + v2 = -6

Solving
-46 + 3v + v2 = -6

Solving for variable 'v'.

Reorder the terms:
-46 + 6 + 3v + v2 = -6 + 6

Combine like terms: -46 + 6 = -40
-40 + 3v + v2 = -6 + 6

Combine like terms: -6 + 6 = 0
-40 + 3v + v2 = 0

Factor a trinomial.
(-8 + -1v)(5 + -1v) = 0

Subproblem 1
Set the factor '(-8 + -1v)' equal to zero and attempt to solve:

Simplifying
-8 + -1v = 0

Solving
-8 + -1v = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1v = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1v = 0 + 8
-1v = 0 + 8

Combine like terms: 0 + 8 = 8
-1v = 8

Divide each side by '-1'.
v = -8

Simplifying
v = -8
Subproblem 2
Set the factor '(5 + -1v)' equal to zero and attempt to solve:

Simplifying
5 + -1v = 0

Solving
5 + -1v = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1v = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1v = 0 + -5
-1v = 0 + -5

Combine like terms: 0 + -5 = -5
-1v = -5

Divide each side by '-1'.
v = 5

Simplifying
v = 5
Solution
v = {-8, 5}