(x^2-8)(x^2-1)=8

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Solution for (x^2-8)(x^2-1)=8 equation: 


Simplifying
(x2 + -8)(x2 + -1) = 8

Reorder the terms:
(-8 + x2)(x2 + -1) = 8

Reorder the terms:
(-8 + x2)(-1 + x2) = 8

Multiply (-8 + x2) * (-1 + x2)
(-8(-1 + x2) + x2(-1 + x2)) = 8
((-1 * -8 + x2 * -8) + x2(-1 + x2)) = 8
((8 + -8x2) + x2(-1 + x2)) = 8
(8 + -8x2 + (-1 * x2 + x2 * x2)) = 8
(8 + -8x2 + (-1x2 + x4)) = 8

Combine like terms: -8x2 + -1x2 = -9x2
(8 + -9x2 + x4) = 8

Add '-8' to each side of the equation.
8 + -9x2 + -8 + x4 = 8 + -8

Reorder the terms:
8 + -8 + -9x2 + x4 = 8 + -8

Combine like terms: 8 + -8 = 0
0 + -9x2 + x4 = 8 + -8
-9x2 + x4 = 8 + -8

Combine like terms: 8 + -8 = 0
-9x2 + x4 = 0

Solving
-9x2 + x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-9 + x2) = 0

Factor a difference between two squares.
x2((3 + x)(-3 + x)) = 0


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

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3

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

Simplifying
-3 + x = 0

Solving
-3 + x = 0

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

Add '3' to each side of the equation.
-3 + 3 + x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + x = 0 + 3
x = 0 + 3

Combine like terms: 0 + 3 = 3
x = 3

Simplifying
x = 3
Solution
x = {0, -3, 3}

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