x(x^2-8)=0

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


Simplifying
x(x2 + -8) = 0

Reorder the terms:
x(-8 + x2) = 0
(-8 * x + x2 * x) = 0
(-8x + x3) = 0

Solving
-8x + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-8 + x2) = 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 + x2)' equal to zero and attempt to solve:

Simplifying
-8 + x2 = 0

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

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

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

Simplifying
x2 = 8

Take the square root of each side:
x = {-2.828427125, 2.828427125}
Solution
x = {0, -2.828427125, 2.828427125}

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