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

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


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

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

Reorder the terms:
-64x2 + x4 + -16(-64 + x2) = 0
-64x2 + x4 + (-64 * -16 + x2 * -16) = 0
-64x2 + x4 + (1024 + -16x2) = 0

Reorder the terms:
1024 + -64x2 + -16x2 + x4 = 0

Combine like terms: -64x2 + -16x2 = -80x2
1024 + -80x2 + x4 = 0

Solving
1024 + -80x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(16 + -1x2)(64 + -1x2) = 0

Factor a difference between two squares.
((4 + x)(4 + -1x))(64 + -1x2) = 0

Factor a difference between two squares.
((8 + x)(8 + -1x))(4 + x)(4 + -1x) = 0


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

Simplifying
4 + x = 0

Solving
4 + x = 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 + x = 0 + -4

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

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

Simplifying
x = -4

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

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 = {-4, 4, -8, 8}

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