x^2(x^2-1)-64(x^2-1)=0

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Solution for x^2(x^2-1)-64(x^2-1)=0 equation:


Simplifying
x2(x2 + -1) + -64(x2 + -1) = 0

Reorder the terms:
x2(-1 + x2) + -64(x2 + -1) = 0
(-1 * x2 + x2 * x2) + -64(x2 + -1) = 0
(-1x2 + x4) + -64(x2 + -1) = 0

Reorder the terms:
-1x2 + x4 + -64(-1 + x2) = 0
-1x2 + x4 + (-1 * -64 + x2 * -64) = 0
-1x2 + x4 + (64 + -64x2) = 0

Reorder the terms:
64 + -1x2 + -64x2 + x4 = 0

Combine like terms: -1x2 + -64x2 = -65x2
64 + -65x2 + x4 = 0

Solving
64 + -65x2 + x4 = 0

Solving for variable 'x'.

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

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

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

Subproblem 1

Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1

Subproblem 2

Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1

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 = {-1, 1, -8, 8}

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