v^4-12v^2+32=0

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Solution for v^4-12v^2+32=0 equation: 


Simplifying
v4 + -12v2 + 32 = 0

Reorder the terms:
32 + -12v2 + v4 = 0

Solving
32 + -12v2 + v4 = 0

Solving for variable 'v'.

Factor a trinomial.
(4 + -1v2)(8 + -1v2) = 0

Factor a difference between two squares.
((2 + v)(2 + -1v))(8 + -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

Take the square root of each side:
v = {-2.828427125, 2.828427125}

Subproblem 2
Set the factor '(2 + v)' equal to zero and attempt to solve:

Simplifying
2 + v = 0

Solving
2 + v = 0

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

Add '-2' to each side of the equation.
2 + -2 + v = 0 + -2

Combine like terms: 2 + -2 = 0
0 + v = 0 + -2
v = 0 + -2

Combine like terms: 0 + -2 = -2
v = -2

Simplifying
v = -2

Subproblem 3
Set the factor '(2 + -1v)' equal to zero and attempt to solve:

Simplifying
2 + -1v = 0

Solving
2 + -1v = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1v = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1v = 0 + -2
-1v = 0 + -2

Combine like terms: 0 + -2 = -2
-1v = -2

Divide each side by '-1'.
v = 2

Simplifying
v = 2
Solution
v = {-2.828427125, 2.828427125, -2, 2}

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