v^2+12=-7v

Solution for v^2+12=-7v equation:

Simplifying
v2 + 12 = -7v

Reorder the terms:
12 + v2 = -7v

Solving
12 + v2 = -7v

Solving for variable 'v'.

Reorder the terms:
12 + 7v + v2 = -7v + 7v

Combine like terms: -7v + 7v = 0
12 + 7v + v2 = 0

Factor a trinomial.
(4 + v)(3 + v) = 0

Subproblem 1
Set the factor '(4 + v)' equal to zero and attempt to solve:

Simplifying
4 + v = 0

Solving
4 + v = 0

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

Add '-4' to each side of the equation.
4 + -4 + v = 0 + -4

Combine like terms: 4 + -4 = 0
0 + v = 0 + -4
v = 0 + -4

Combine like terms: 0 + -4 = -4
v = -4

Simplifying
v = -4
Subproblem 2
Set the factor '(3 + v)' equal to zero and attempt to solve:

Simplifying
3 + v = 0

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

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

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

Simplifying
v = -3
Solution
v = {-4, -3}