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

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


Simplifying
X2(X2 + -16) + -64(X2 + -16) = 0

Reorder the terms:
X2(-16 + X2) + -64(X2 + -16) = 0
(-16 * X2 + X2 * X2) + -64(X2 + -16) = 0
(-16X2 + X4) + -64(X2 + -16) = 0

Reorder the terms:
-16X2 + X4 + -64(-16 + X2) = 0
-16X2 + X4 + (-16 * -64 + X2 * -64) = 0
-16X2 + X4 + (1024 + -64X2) = 0

Reorder the terms:
1024 + -16X2 + -64X2 + X4 = 0

Combine like terms: -16X2 + -64X2 = -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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