y^6-625y^2=0

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Solution for y^6-625y^2=0 equation: 


Simplifying
y6 + -625y2 = 0

Reorder the terms:
-625y2 + y6 = 0

Solving
-625y2 + y6 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y2'.
y2(-625 + y4) = 0

Factor a difference between two squares.
y2((25 + y2)(-25 + y2)) = 0

Factor a difference between two squares.
y2((25 + y2)((5 + y)(-5 + y))) = 0


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 '(25 + y2)' equal to zero and attempt to solve:

Simplifying
25 + y2 = 0

Solving
25 + y2 = 0

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

Add '-25' to each side of the equation.
25 + -25 + y2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + y2 = 0 + -25
y2 = 0 + -25

Combine like terms: 0 + -25 = -25
y2 = -25

Simplifying
y2 = -25

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 3
Set the factor '(5 + y)' equal to zero and attempt to solve:

Simplifying
5 + y = 0

Solving
5 + y = 0

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

Add '-5' to each side of the equation.
5 + -5 + y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + y = 0 + -5
y = 0 + -5

Combine like terms: 0 + -5 = -5
y = -5

Simplifying
y = -5

Subproblem 4
Set the factor '(-5 + y)' equal to zero and attempt to solve:

Simplifying
-5 + y = 0

Solving
-5 + y = 0

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

Add '5' to each side of the equation.
-5 + 5 + y = 0 + 5

Combine like terms: -5 + 5 = 0
0 + y = 0 + 5
y = 0 + 5

Combine like terms: 0 + 5 = 5
y = 5

Simplifying
y = 5
Solution
y = {0, -5, 5}

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