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

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


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

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

Reorder the terms:
-64x2 + x4 + -4(-64 + x2) = 0
-64x2 + x4 + (-64 * -4 + x2 * -4) = 0
-64x2 + x4 + (256 + -4x2) = 0

Reorder the terms:
256 + -64x2 + -4x2 + x4 = 0

Combine like terms: -64x2 + -4x2 = -68x2
256 + -68x2 + x4 = 0

Solving
256 + -68x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(4 + -1x2)(64 + -1x2) = 0

Factor a difference between two squares.
((2 + x)(2 + -1x))(64 + -1x2) = 0

Factor a difference between two squares.
((8 + x)(8 + -1x))(2 + x)(2 + -1x) = 0


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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

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

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

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

Simplifying
x = 2

Subproblem 3
Set the factor '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 0

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

Add '-8' to each side of the equation.
8 + -8 + x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Simplifying
x = -8

Subproblem 4
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-2, 2, -8, 8}

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