0=16x^7-200x^5+625x^3

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Solution for 0=16x^7-200x^5+625x^3 equation: 


Simplifying
0 = 16x7 + -200x5 + 625x3

Reorder the terms:
0 = 625x3 + -200x5 + 16x7

Solving
0 = 625x3 + -200x5 + 16x7

Solving for variable 'x'.
Remove the zero:
-625x3 + 200x5 + -16x7 = 625x3 + -200x5 + 16x7 + -625x3 + 200x5 + -16x7

Reorder the terms:
-625x3 + 200x5 + -16x7 = 625x3 + -625x3 + -200x5 + 200x5 + 16x7 + -16x7

Combine like terms: 625x3 + -625x3 = 0
-625x3 + 200x5 + -16x7 = 0 + -200x5 + 200x5 + 16x7 + -16x7
-625x3 + 200x5 + -16x7 = -200x5 + 200x5 + 16x7 + -16x7

Combine like terms: -200x5 + 200x5 = 0
-625x3 + 200x5 + -16x7 = 0 + 16x7 + -16x7
-625x3 + 200x5 + -16x7 = 16x7 + -16x7

Combine like terms: 16x7 + -16x7 = 0
-625x3 + 200x5 + -16x7 = 0

Factor out the Greatest Common Factor (GCF), 'x3'.
x3(-625 + 200x2 + -16x4) = 0

Factor a trinomial.
x3((-25 + 4x2)(25 + -4x2)) = 0

Factor a difference between two squares.
x3(((5 + 2x)(-5 + 2x))(25 + -4x2)) = 0

Factor a difference between two squares.
x3(((5 + 2x)(5 + -2x))(5 + 2x)(-5 + 2x)) = 0


Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve:

Simplifying
x3 = 0

Solving
x3 = 0

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

Simplifying
x3 = 0

The solution to this equation could not be determined.

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

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

Simplifying
5 + 2x = 0

Solving
5 + 2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + 2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2x = 0 + -5
2x = 0 + -5

Combine like terms: 0 + -5 = -5
2x = -5

Divide each side by '2'.
x = -2.5

Simplifying
x = -2.5

Subproblem 3
Set the factor '(-5 + 2x)' equal to zero and attempt to solve:

Simplifying
-5 + 2x = 0

Solving
-5 + 2x = 0

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

Add '5' to each side of the equation.
-5 + 5 + 2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 2x = 0 + 5
2x = 0 + 5

Combine like terms: 0 + 5 = 5
2x = 5

Divide each side by '2'.
x = 2.5

Simplifying
x = 2.5

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

Simplifying
5 + 2x = 0

Solving
5 + 2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + 2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2x = 0 + -5
2x = 0 + -5

Combine like terms: 0 + -5 = -5
2x = -5

Divide each side by '2'.
x = -2.5

Simplifying
x = -2.5

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

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {-2.5, 2.5, -2.5, 2.5}

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