y^4-676y^2+57600=0

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Solution for y^4-676y^2+57600=0 equation: 


Simplifying
y4 + -676y2 + 57600 = 0

Reorder the terms:
57600 + -676y2 + y4 = 0

Solving
57600 + -676y2 + y4 = 0

Solving for variable 'y'.

Factor a trinomial.
(100 + -1y2)(576 + -1y2) = 0

Factor a difference between two squares.
((10 + y)(10 + -1y))(576 + -1y2) = 0

Factor a difference between two squares.
((24 + y)(24 + -1y))(10 + y)(10 + -1y) = 0


Subproblem 1
Set the factor '(10 + y)' equal to zero and attempt to solve:

Simplifying
10 + y = 0

Solving
10 + y = 0

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

Add '-10' to each side of the equation.
10 + -10 + y = 0 + -10

Combine like terms: 10 + -10 = 0
0 + y = 0 + -10
y = 0 + -10

Combine like terms: 0 + -10 = -10
y = -10

Simplifying
y = -10

Subproblem 2
Set the factor '(10 + -1y)' equal to zero and attempt to solve:

Simplifying
10 + -1y = 0

Solving
10 + -1y = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1y = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1y = 0 + -10
-1y = 0 + -10

Combine like terms: 0 + -10 = -10
-1y = -10

Divide each side by '-1'.
y = 10

Simplifying
y = 10

Subproblem 3
Set the factor '(24 + y)' equal to zero and attempt to solve:

Simplifying
24 + y = 0

Solving
24 + y = 0

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

Add '-24' to each side of the equation.
24 + -24 + y = 0 + -24

Combine like terms: 24 + -24 = 0
0 + y = 0 + -24
y = 0 + -24

Combine like terms: 0 + -24 = -24
y = -24

Simplifying
y = -24

Subproblem 4
Set the factor '(24 + -1y)' equal to zero and attempt to solve:

Simplifying
24 + -1y = 0

Solving
24 + -1y = 0

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

Add '-24' to each side of the equation.
24 + -24 + -1y = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -1y = 0 + -24
-1y = 0 + -24

Combine like terms: 0 + -24 = -24
-1y = -24

Divide each side by '-1'.
y = 24

Simplifying
y = 24
Solution
y = {-10, 10, -24, 24}

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