27y^6+9y^2+12y^4=

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Solution for 27y^6+9y^2+12y^4= equation: 


Simplifying
27y6 + 9y2 + 12y4 = 0

Reorder the terms:
9y2 + 12y4 + 27y6 = 0

Solving
9y2 + 12y4 + 27y6 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3y2'.
3y2(3 + 4y2 + 9y4) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'y2' equal to zero and attempt to solve:

Simplifying
y2 = 0

Solving
y2 = 0

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

Simplifying
y2 = 0

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

Subproblem 2
Set the factor '(3 + 4y2 + 9y4)' equal to zero and attempt to solve:

Simplifying
3 + 4y2 + 9y4 = 0

Solving
3 + 4y2 + 9y4 = 0

Begin completing the square.  Divide all terms by
9 the coefficient of the squared term: 

Divide each side by '9'.
0.3333333333 + 0.4444444444y2 + y4 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + 0.4444444444y2 + -0.3333333333 + y4 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + 0.4444444444y2 + y4 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + 0.4444444444y2 + y4 = 0 + -0.3333333333
0.4444444444y2 + y4 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
0.4444444444y2 + y4 = -0.3333333333

The y term is 0.4444444444y2.  Take half its coefficient (0.2222222222).
Square it (0.04938271604) and add it to both sides.

Add '0.04938271604' to each side of the equation.
0.4444444444y2 + 0.04938271604 + y4 = -0.3333333333 + 0.04938271604

Reorder the terms:
0.04938271604 + 0.4444444444y2 + y4 = -0.3333333333 + 0.04938271604

Combine like terms: -0.3333333333 + 0.04938271604 = -0.28395061726
0.04938271604 + 0.4444444444y2 + y4 = -0.28395061726

Factor a perfect square on the left side:
(y2 + 0.2222222222)(y2 + 0.2222222222) = -0.28395061726

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
y = {0}

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