x(x^2-2x)=x^3-8

Solution for x(x^2-2x)=x^3-8 equation:

Simplifying
x(x2 + -2x) = x3 + -8

Reorder the terms:
x(-2x + x2) = x3 + -8
(-2x * x + x2 * x) = x3 + -8
(-2x2 + x3) = x3 + -8

Reorder the terms:
-2x2 + x3 = -8 + x3

Add '-1x3' to each side of the equation.
-2x2 + x3 + -1x3 = -8 + x3 + -1x3

Combine like terms: x3 + -1x3 = 0
-2x2 + 0 = -8 + x3 + -1x3
-2x2 = -8 + x3 + -1x3

Combine like terms: x3 + -1x3 = 0
-2x2 = -8 + 0
-2x2 = -8

Solving
-2x2 = -8

Solving for variable 'x'.

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

Divide each side by '-2'.
x2 = 4

Simplifying
x2 = 4

Take the square root of each side:
x = {-2, 2}