3v^6-9v^4+147v^2=0

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Solution for 3v^6-9v^4+147v^2=0 equation: 


Simplifying
3v6 + -9v4 + 147v2 = 0

Reorder the terms:
147v2 + -9v4 + 3v6 = 0

Solving
147v2 + -9v4 + 3v6 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '3v2'.
3v2(49 + -3v2 + v4) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'v2' equal to zero and attempt to solve:

Simplifying
v2 = 0

Solving
v2 = 0

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

Simplifying
v2 = 0

Take the square root of each side:
v = {0}

Subproblem 2
Set the factor '(49 + -3v2 + v4)' equal to zero and attempt to solve:

Simplifying
49 + -3v2 + v4 = 0

Solving
49 + -3v2 + v4 = 0

Begin completing the square.

Move the constant term to the right:

Add '-49' to each side of the equation.
49 + -3v2 + -49 + v4 = 0 + -49

Reorder the terms:
49 + -49 + -3v2 + v4 = 0 + -49

Combine like terms: 49 + -49 = 0
0 + -3v2 + v4 = 0 + -49
-3v2 + v4 = 0 + -49

Combine like terms: 0 + -49 = -49
-3v2 + v4 = -49

The v term is -3v2.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3v2 + 2.25 + v4 = -49 + 2.25

Reorder the terms:
2.25 + -3v2 + v4 = -49 + 2.25

Combine like terms: -49 + 2.25 = -46.75
2.25 + -3v2 + v4 = -46.75

Factor a perfect square on the left side:
(v2 + -1.5)(v2 + -1.5) = -46.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
v = {0}

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