0=5[(X^2)(X-2)]

Solution for 0=5[(X^2)(X-2)] equation:

Simplifying
0 = 5[(X2)(X + -2)]

Reorder the terms:
0 = 5[X2(-2 + X)]
0 = 5[(-2 * X2 + X * X2)]
0 = 5[(-2X2 + X3)]
0 = [-2X2 * 5 + X3 * 5]
0 = [-10X2 + 5X3]

Solving
0 = -10X2 + 5X3

Solving for variable 'X'.
Remove the zero:
10X2 + -5X3 = -10X2 + 5X3 + 10X2 + -5X3

Reorder the terms:
10X2 + -5X3 = -10X2 + 10X2 + 5X3 + -5X3

Combine like terms: -10X2 + 10X2 = 0
10X2 + -5X3 = 0 + 5X3 + -5X3
10X2 + -5X3 = 5X3 + -5X3

Combine like terms: 5X3 + -5X3 = 0
10X2 + -5X3 = 0

Factor out the Greatest Common Factor (GCF), '5X2'.
5X2(2 + -1X) = 0

Ignore the factor 5.
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}