v^2+2v-31=4

Solution for v^2+2v-31=4 equation:

Simplifying
v2 + 2v + -31 = 4

Reorder the terms:
-31 + 2v + v2 = 4

Solving
-31 + 2v + v2 = 4

Solving for variable 'v'.

Reorder the terms:
-31 + -4 + 2v + v2 = 4 + -4

Combine like terms: -31 + -4 = -35
-35 + 2v + v2 = 4 + -4

Combine like terms: 4 + -4 = 0
-35 + 2v + v2 = 0

Factor a trinomial.
(-7 + -1v)(5 + -1v) = 0

Subproblem 1
Set the factor '(-7 + -1v)' equal to zero and attempt to solve:

Simplifying
-7 + -1v = 0

Solving
-7 + -1v = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1v = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1v = 0 + 7
-1v = 0 + 7

Combine like terms: 0 + 7 = 7
-1v = 7

Divide each side by '-1'.
v = -7

Simplifying
v = -7
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 = {-7, 5}