v^2+48=-14v

Solution for v^2+48=-14v equation:

Simplifying
v2 + 48 = -14v

Reorder the terms:
48 + v2 = -14v

Solving
48 + v2 = -14v

Solving for variable 'v'.

Reorder the terms:
48 + 14v + v2 = -14v + 14v

Combine like terms: -14v + 14v = 0
48 + 14v + v2 = 0

Factor a trinomial.
(8 + v)(6 + v) = 0

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

Simplifying
8 + v = 0

Solving
8 + v = 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 + v = 0 + -8

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

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

Simplifying
v = -8
Subproblem 2
Set the factor '(6 + v)' equal to zero and attempt to solve:

Simplifying
6 + v = 0

Solving
6 + v = 0

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

Add '-6' to each side of the equation.
6 + -6 + v = 0 + -6

Combine like terms: 6 + -6 = 0
0 + v = 0 + -6
v = 0 + -6

Combine like terms: 0 + -6 = -6
v = -6

Simplifying
v = -6
Solution
v = {-8, -6}