0=25y^4-100y^2

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Solution for 0=25y^4-100y^2 equation: 


Simplifying
0 = 25y4 + -100y2

Reorder the terms:
0 = -100y2 + 25y4

Solving
0 = -100y2 + 25y4

Solving for variable 'y'.
Remove the zero:
100y2 + -25y4 = -100y2 + 25y4 + 100y2 + -25y4

Reorder the terms:
100y2 + -25y4 = -100y2 + 100y2 + 25y4 + -25y4

Combine like terms: -100y2 + 100y2 = 0
100y2 + -25y4 = 0 + 25y4 + -25y4
100y2 + -25y4 = 25y4 + -25y4

Combine like terms: 25y4 + -25y4 = 0
100y2 + -25y4 = 0

Factor out the Greatest Common Factor (GCF), '25y2'.
25y2(4 + -1y2) = 0

Factor a difference between two squares.
25y2((2 + y)(2 + -1y)) = 0

Ignore the factor 25.

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 '(2 + y)' equal to zero and attempt to solve:

Simplifying
2 + y = 0

Solving
2 + y = 0

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

Add '-2' to each side of the equation.
2 + -2 + y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + y = 0 + -2
y = 0 + -2

Combine like terms: 0 + -2 = -2
y = -2

Simplifying
y = -2

Subproblem 3
Set the factor '(2 + -1y)' equal to zero and attempt to solve:

Simplifying
2 + -1y = 0

Solving
2 + -1y = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1y = 0 + -2
-1y = 0 + -2

Combine like terms: 0 + -2 = -2
-1y = -2

Divide each side by '-1'.
y = 2

Simplifying
y = 2
Solution
y = {0, -2, 2}

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