0=(6x^2)-(6x)

Solution for 0=(6x^2)-(6x) equation:

Simplifying
0 = (6x2) + -1(6x)

Remove parenthesis around (6x)
0 = (6x2) + -1 * 6x

Multiply -1 * 6
0 = (6x2) + -6x

Reorder the terms:
0 = -6x + (6x2)

Solving
0 = -6x + (6x2)

Solving for variable 'x'.
Remove the zero:
6x + (-6x2) = -6x + (6x2) + 6x + (-6x2)

Reorder the terms:
6x + (-6x2) = -6x + 6x + (6x2) + (-6x2)

Combine like terms: -6x + 6x = 0
6x + (-6x2) = 0 + (6x2) + (-6x2)
6x + (-6x2) = (6x2) + (-6x2)

Combine like terms: (6x2) + (-6x2) = 0
6x + (-6x2) = 0

Factor out the Greatest Common Factor (GCF), '6x'.
6x(1 + (-1x)) = 0

Ignore the factor 6.
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}