0=x(5-20x^2+16x^4)

Solution for 0=x(5-20x^2+16x^4) equation:

Simplifying
0 = x(5 + -20x2 + 16x4)
0 = (5 * x + -20x2 * x + 16x4 * x)
0 = (5x + -20x3 + 16x5)

Solving
0 = 5x + -20x3 + 16x5

Solving for variable 'x'.
Remove the zero:
-5x + 20x3 + -16x5 = 5x + -20x3 + 16x5 + -5x + 20x3 + -16x5

Reorder the terms:
-5x + 20x3 + -16x5 = 5x + -5x + -20x3 + 20x3 + 16x5 + -16x5

Combine like terms: 5x + -5x = 0
-5x + 20x3 + -16x5 = 0 + -20x3 + 20x3 + 16x5 + -16x5
-5x + 20x3 + -16x5 = -20x3 + 20x3 + 16x5 + -16x5

Combine like terms: -20x3 + 20x3 = 0
-5x + 20x3 + -16x5 = 0 + 16x5 + -16x5
-5x + 20x3 + -16x5 = 16x5 + -16x5

Combine like terms: 16x5 + -16x5 = 0
-5x + 20x3 + -16x5 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-5 + 20x2 + -16x4) = 0

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-5 + 20x2 + -16x4)' equal to zero and attempt to solve:

Simplifying
-5 + 20x2 + -16x4 = 0

Solving
-5 + 20x2 + -16x4 = 0

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
0.3125 + -1.25x2 + x4 = 0

Move the constant term to the right:

Add '-0.3125' to each side of the equation.
0.3125 + -1.25x2 + -0.3125 + x4 = 0 + -0.3125

Reorder the terms:
0.3125 + -0.3125 + -1.25x2 + x4 = 0 + -0.3125

Combine like terms: 0.3125 + -0.3125 = 0.0000
0.0000 + -1.25x2 + x4 = 0 + -0.3125
-1.25x2 + x4 = 0 + -0.3125

Combine like terms: 0 + -0.3125 = -0.3125
-1.25x2 + x4 = -0.3125

The x term is -1.25x2.  Take half its coefficient (-0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
-1.25x2 + 0.390625 + x4 = -0.3125 + 0.390625

Reorder the terms:
0.390625 + -1.25x2 + x4 = -0.3125 + 0.390625

Combine like terms: -0.3125 + 0.390625 = 0.078125
0.390625 + -1.25x2 + x4 = 0.078125

Factor a perfect square on the left side:
(x2 + -0.625)(x2 + -0.625) = 0.078125

Calculate the square root of the right side: 0.279508497

Break this problem into two subproblems by setting 
(x2 + -0.625) equal to 0.279508497 and -0.279508497.

Subproblem 1
x2 + -0.625 = 0.279508497

Simplifying
x2 + -0.625 = 0.279508497

Reorder the terms:
-0.625 + x2 = 0.279508497

Solving
-0.625 + x2 = 0.279508497

Solving for variable 'x'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + x2 = 0.279508497 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + x2 = 0.279508497 + 0.625
x2 = 0.279508497 + 0.625

Combine like terms: 0.279508497 + 0.625 = 0.904508497
x2 = 0.904508497

Simplifying
x2 = 0.904508497

Take the square root of each side:
x = {-0.951056516, 0.951056516}

Subproblem 2
x2 + -0.625 = -0.279508497

Simplifying
x2 + -0.625 = -0.279508497

Reorder the terms:
-0.625 + x2 = -0.279508497

Solving
-0.625 + x2 = -0.279508497

Solving for variable 'x'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + x2 = -0.279508497 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + x2 = -0.279508497 + 0.625
x2 = -0.279508497 + 0.625

Combine like terms: -0.279508497 + 0.625 = 0.345491503
x2 = 0.345491503

Simplifying
x2 = 0.345491503

Take the square root of each side:
x = {-0.587785252, 0.587785252}

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.951056516, 0.951056516, -0.587785252, 0.587785252}
Solution
x = {0, -0.951056516, 0.951056516, -0.587785252, 0.587785252}