y^4-72y^2+512=0

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Solution for y^4-72y^2+512=0 equation: 


Simplifying
y4 + -72y2 + 512 = 0

Reorder the terms:
512 + -72y2 + y4 = 0

Solving
512 + -72y2 + y4 = 0

Solving for variable 'y'.

Factor a trinomial.
(8 + -1y2)(64 + -1y2) = 0

Factor a difference between two squares.
(8 + -1y2)((8 + y)(8 + -1y)) = 0


Subproblem 1
Set the factor '(8 + -1y2)' equal to zero and attempt to solve:

Simplifying
8 + -1y2 = 0

Solving
8 + -1y2 = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1y2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1y2 = 0 + -8
-1y2 = 0 + -8

Combine like terms: 0 + -8 = -8
-1y2 = -8

Divide each side by '-1'.
y2 = 8

Simplifying
y2 = 8

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

Subproblem 2
Set the factor '(8 + y)' equal to zero and attempt to solve:

Simplifying
8 + y = 0

Solving
8 + y = 0

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

Add '-8' to each side of the equation.
8 + -8 + y = 0 + -8

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

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

Simplifying
y = -8

Subproblem 3
Set the factor '(8 + -1y)' equal to zero and attempt to solve:

Simplifying
8 + -1y = 0

Solving
8 + -1y = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1y = 0 + -8

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

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

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

Simplifying
y = 8
Solution
y = {-2.828427125, 2.828427125, -8, 8}

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