0=25x^4-16x^2

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Solution for 0=25x^4-16x^2 equation: 


Simplifying
0 = 25x4 + -16x2

Reorder the terms:
0 = -16x2 + 25x4

Solving
0 = -16x2 + 25x4

Solving for variable 'x'.
Remove the zero:
16x2 + -25x4 = -16x2 + 25x4 + 16x2 + -25x4

Reorder the terms:
16x2 + -25x4 = -16x2 + 16x2 + 25x4 + -25x4

Combine like terms: -16x2 + 16x2 = 0
16x2 + -25x4 = 0 + 25x4 + -25x4
16x2 + -25x4 = 25x4 + -25x4

Combine like terms: 25x4 + -25x4 = 0
16x2 + -25x4 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(16 + -25x2) = 0

Factor a difference between two squares.
x2((4 + 5x)(4 + -5x)) = 0


Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

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

Subproblem 2
Set the factor '(4 + 5x)' equal to zero and attempt to solve:

Simplifying
4 + 5x = 0

Solving
4 + 5x = 0

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

Add '-4' to each side of the equation.
4 + -4 + 5x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 5x = 0 + -4
5x = 0 + -4

Combine like terms: 0 + -4 = -4
5x = -4

Divide each side by '5'.
x = -0.8

Simplifying
x = -0.8

Subproblem 3
Set the factor '(4 + -5x)' equal to zero and attempt to solve:

Simplifying
4 + -5x = 0

Solving
4 + -5x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5x = 0 + -4
-5x = 0 + -4

Combine like terms: 0 + -4 = -4
-5x = -4

Divide each side by '-5'.
x = 0.8

Simplifying
x = 0.8
Solution
x = {0, -0.8, 0.8}

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