v^4+2v^2-48=

Solution for v^4+2v^2-48= equation:

Simplifying
v4 + 2v2 + -48 = 0

Reorder the terms:
-48 + 2v2 + v4 = 0

Solving
-48 + 2v2 + v4 = 0

Solving for variable 'v'.

Factor a trinomial.
(-8 + -1v2)(6 + -1v2) = 0

Subproblem 1
Set the factor '(-8 + -1v2)' equal to zero and attempt to solve:

Simplifying
-8 + -1v2 = 0

Solving
-8 + -1v2 = 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 + -1v2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1v2 = 0 + 8
-1v2 = 0 + 8

Combine like terms: 0 + 8 = 8
-1v2 = 8

Divide each side by '-1'.
v2 = -8

Simplifying
v2 = -8

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(6 + -1v2)' equal to zero and attempt to solve:

Simplifying
6 + -1v2 = 0

Solving
6 + -1v2 = 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 + -1v2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1v2 = 0 + -6
-1v2 = 0 + -6

Combine like terms: 0 + -6 = -6
-1v2 = -6

Divide each side by '-1'.
v2 = 6

Simplifying
v2 = 6

Take the square root of each side:
v = {-2.449489743, 2.449489743}
Solution
v = {-2.449489743, 2.449489743}