6x^2(x^3-2)=

Solution for 6x^2(x^3-2)= equation:

Simplifying
6x2(x3 + -2) = 0

Reorder the terms:
6x2(-2 + x3) = 0
(-2 * 6x2 + x3 * 6x2) = 0
(-12x2 + 6x5) = 0

Solving
-12x2 + 6x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6x2'.
6x2(-2 + x3) = 0

Ignore the factor 6.
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 '(-2 + x3)' equal to zero and attempt to solve:

Simplifying
-2 + x3 = 0

Solving
-2 + x3 = 0

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

Add '2' to each side of the equation.
-2 + 2 + x3 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + x3 = 0 + 2
x3 = 0 + 2

Combine like terms: 0 + 2 = 2
x3 = 2

Simplifying
x3 = 2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}