(x^2-8)(x^2-9)=0

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Solution for (x^2-8)(x^2-9)=0 equation: 


Simplifying
(x2 + -8)(x2 + -9) = 0

Reorder the terms:
(-8 + x2)(x2 + -9) = 0

Reorder the terms:
(-8 + x2)(-9 + x2) = 0

Multiply (-8 + x2) * (-9 + x2)
(-8(-9 + x2) + x2(-9 + x2)) = 0
((-9 * -8 + x2 * -8) + x2(-9 + x2)) = 0
((72 + -8x2) + x2(-9 + x2)) = 0
(72 + -8x2 + (-9 * x2 + x2 * x2)) = 0
(72 + -8x2 + (-9x2 + x4)) = 0

Combine like terms: -8x2 + -9x2 = -17x2
(72 + -17x2 + x4) = 0

Solving
72 + -17x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(8 + -1x2)(9 + -1x2) = 0

Factor a difference between two squares.
(8 + -1x2)((3 + x)(3 + -1x)) = 0


Subproblem 1
Set the factor '(8 + -1x2)' equal to zero and attempt to solve:

Simplifying
8 + -1x2 = 0

Solving
8 + -1x2 = 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 + -1x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x2 = 0 + -8
-1x2 = 0 + -8

Combine like terms: 0 + -8 = -8
-1x2 = -8

Divide each side by '-1'.
x2 = 8

Simplifying
x2 = 8

Take the square root of each side:
x = {-2.828427125, 2.828427125}

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 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-2.828427125, 2.828427125, -3, 3}

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