16x^2+4(x^4-4x^2-4x^2+16)-64=0

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Solution for 16x^2+4(x^4-4x^2-4x^2+16)-64=0 equation: 


Simplifying
16x2 + 4(x4 + -4x2 + -4x2 + 16) + -64 = 0

Reorder the terms:
16x2 + 4(16 + -4x2 + -4x2 + x4) + -64 = 0

Combine like terms: -4x2 + -4x2 = -8x2
16x2 + 4(16 + -8x2 + x4) + -64 = 0
16x2 + (16 * 4 + -8x2 * 4 + x4 * 4) + -64 = 0
16x2 + (64 + -32x2 + 4x4) + -64 = 0

Reorder the terms:
64 + -64 + 16x2 + -32x2 + 4x4 = 0

Combine like terms: 64 + -64 = 0
0 + 16x2 + -32x2 + 4x4 = 0
16x2 + -32x2 + 4x4 = 0

Combine like terms: 16x2 + -32x2 = -16x2
-16x2 + 4x4 = 0

Solving
-16x2 + 4x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x2'.
4x2(-4 + x2) = 0

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

Ignore the factor 4.

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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

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

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

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

Simplifying
x = -2

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

Simplifying
-2 + x = 0

Solving
-2 + x = 0

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

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

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

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

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

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