0=24x(x-1)

Solution for 0=24x(x-1) equation:

Simplifying
0 = 24x(x + -1)

Reorder the terms:
0 = 24x(-1 + x)
0 = (-1 * 24x + x * 24x)
0 = (-24x + 24x2)

Solving
0 = -24x + 24x2

Solving for variable 'x'.
Remove the zero:
24x + -24x2 = -24x + 24x2 + 24x + -24x2

Reorder the terms:
24x + -24x2 = -24x + 24x + 24x2 + -24x2

Combine like terms: -24x + 24x = 0
24x + -24x2 = 0 + 24x2 + -24x2
24x + -24x2 = 24x2 + -24x2

Combine like terms: 24x2 + -24x2 = 0
24x + -24x2 = 0

Factor out the Greatest Common Factor (GCF), '24x'.
24x(1 + -1x) = 0

Ignore the factor 24.
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 '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {0, 1}