0=X^2(X-2)

Solution for 0=X^2(X-2) equation:

Simplifying
0 = X2(X + -2)

Reorder the terms:
0 = X2(-2 + X)
0 = (-2 * X2 + X * X2)
0 = (-2X2 + X3)

Solving
0 = -2X2 + X3

Solving for variable 'X'.
Remove the zero:
2X2 + -1X3 = -2X2 + X3 + 2X2 + -1X3

Reorder the terms:
2X2 + -1X3 = -2X2 + 2X2 + X3 + -1X3

Combine like terms: -2X2 + 2X2 = 0
2X2 + -1X3 = 0 + X3 + -1X3
2X2 + -1X3 = X3 + -1X3

Combine like terms: X3 + -1X3 = 0
2X2 + -1X3 = 0

Factor out the Greatest Common Factor (GCF), 'X2'.
X2(2 + -1X) = 0

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

Simplifying
2 + -1X = 0

Solving
2 + -1X = 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 + -1X = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1X = 0 + -2
-1X = 0 + -2

Combine like terms: 0 + -2 = -2
-1X = -2

Divide each side by '-1'.
X = 2

Simplifying
X = 2
Solution
X = {0, 2}