x(x^2-6)(x^2+8)=0

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Solution for x(x^2-6)(x^2+8)=0 equation: 


Simplifying
x(x2 + -6)(x2 + 8) = 0

Reorder the terms:
x(-6 + x2)(x2 + 8) = 0

Reorder the terms:
x(-6 + x2)(8 + x2) = 0

Multiply (-6 + x2) * (8 + x2)
x(-6(8 + x2) + x2(8 + x2)) = 0
x((8 * -6 + x2 * -6) + x2(8 + x2)) = 0
x((-48 + -6x2) + x2(8 + x2)) = 0
x(-48 + -6x2 + (8 * x2 + x2 * x2)) = 0
x(-48 + -6x2 + (8x2 + x4)) = 0

Combine like terms: -6x2 + 8x2 = 2x2
x(-48 + 2x2 + x4) = 0
(-48 * x + 2x2 * x + x4 * x) = 0
(-48x + 2x3 + x5) = 0

Solving
-48x + 2x3 + x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-48 + 2x2 + x4) = 0

Factor a trinomial.
x((-8 + -1x2)(6 + -1x2)) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
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

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 3
Set the factor '(6 + -1x2)' equal to zero and attempt to solve:

Simplifying
6 + -1x2 = 0

Solving
6 + -1x2 = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x2 = 0 + -6
-1x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-1x2 = -6

Divide each side by '-1'.
x2 = 6

Simplifying
x2 = 6

Take the square root of each side:
x = {-2.449489743, 2.449489743}
Solution
x = {0, -2.449489743, 2.449489743}

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